What about unrequited love triangles, where a person does not consummate the relationship with the third person because they are already committed?
I find this type of love-triangle to be very powerful and tragic. Not every love triangle is a classic Lancelot-Arthur-Gwenuevere type of love triangle.
Don’t forget there can be a satisfying ending to Romance Rivalries. SPOILER ALERT!!! My faves include-
Pirates of the Caribbean Curse of the Black Pearl- ‘This is a fine sword, blacksmith. I expect the man who made it to take as good care of everything else important to him.’ [Norrington looks pointedly at his former fiancée]
Frozen. Turns out the rival was never interested in Romance and now the prick is getting his comeuppance.
Mistborn Second Series. The main socially acceptable Romance character turns out to be just as interesting a character as the rival and the hero likes her. Still need the rival to get someone but the series isn’t over yet.
Enchanted- ‘I see now I was never the Princess’s True Love. Hey, your fiancée is hot and now she’s available!’
There’s lots of other ways it can work including the possibility of a three-way Romance 
(can’t think of an example offhand). But it has to be written well, on that I can agree.
It can become quite shallow when NPCs are obviously just waiting for you to ‘take your pick’.
This so much!
When I play a game that has RO’s of course I’d like the option of getting the one I want, but it can feel incredibly boring when the RO is MC sexual and you don’t have to put in any effort to make them like you.
As an ace, I’m not as interested in engaging in love triangles, so I might be a little biased.
I’ll give some feedback as a writer though at a later point!
Personally, whenever I encounter a love triangle in fiction, my automatic thought process turns to polyamory. I polyship almost all love polygons that involve characters I like. Of course, the reason this works is because fiction and reality are fundamentally different. In reality, some (most?) people just aren’t suited to poly relationships, and what’s more, just because A and B are both attracted to C, doesn’t mean they can get along well with each other.
But yeah, if I encountered an RO in a game that had another partner/suitor, I’d be more interested in a poly option than in “winning” them.
Clearly the best option is to have most of your characters in pre-established relationships and have most of them available only after an unfortunate accident or driving the couple apart 
humm…then you have a new problem ! ‘Aw man…they sure bounced back fast from that break up huh! WOw…we just buried X and they are already trying to get in mah pants’
It just means they get over tragedy quickly 
I know in a story , you can’t do day by day…and make it go a couple of years . Cose then…you be dead and someone has to write the ending for you lol
But…it make me think , that some ‘childhood romance’ for exemple , (they really arent bad) if expanded on…would be great .
And introducing for exemple , someone who is a widow for exemple…(not just dead 5min ago!!!)…but you know , being a widow for a couple of years and such . Give romance a new spin .
This would be really interesting depending on how it’s pulled off. There could be underlying tension between the MC and the RO, or the MC could just be “flawed” in a way that the RO gets fed up with their shit and chooses the rival instead.
Fallen Hero by malinryden and Guenevere (of course, it would be Arthur-Gwen-and-Lancelot) by jeantown really pull this off well.
The one time I remember outright hating a “romantic rival”: If you choose to romance Fenris in DA:2 and take him with you on a specific Anders quest, Anders will take you aside and berate you for romancing Fenris. I suppose that lots of my hate for Anders also comes with the fact that he’s always interested in Hawke and that he never stops pining for them, regardless of how much or little attention you give him. I’ve always found it somewhat uncomfortable. (Same with Liara in ME3, who somehow still seems to think she has a chance with Shepard as long as you don’t have your romantic choice locked in.)
However, I seem to remember loving whenever jealousy came up in the DA:O party banter. What made it particularly enjoyable for me, was the impression that the companions had relationships and an inner life outside of their interactions with my warden. And the fact that I didn’t necessarily have to deal with the jealousy that was displayed in their banter. Because, while jealousy is all fun when it comes up in random banters, I always dread when characters give me the final “Choose one of us!” speech.
Since Fallen Hero got mentioned: I’m super looking forward to how things will develop between my (so far) Ortega-romancing MC and stupid, sexy Herald with his obvious crush in FH2. And while the majority of my MCs tend to be nice-ish do-gooders, damn, I can’t wait to corrupt Herald a little.
I would think this is an excellent idea for story telling since it is very refreshing … imagine we recruit 2 companions to our team, and they are attracted to each other, if MC do not intervene they develop into a couple automatically , but if MC is also interested in one of them, MC need to compete for the hand of one of the RO with another RO … if we fail in our courtship , we can decide whether we hold grudge to them or embrace them with well wishes 
It will be even more interesting if the MC’s rival meet with a danger and the RO who MC tries to court request MC to save him/her , the story can make MC decides whether he/she wants to eliminate their competition by refusing to save the rival… Or still saving the rival out of humanity but has to endure watching the rival and love interest living happily ever after … this ultimately make a touching lovely story :-)
I remember watching some movie similar with this plotline , where in the end … in order to thank the protagonist for saving her chosen one, the girl want the protagonist to be their future child’s guardian :-)
I think a lot more people are “suited” to polyamory than we realize, just as more and more people dare to openly admit their sexuality and come out as gay, lesbian or especially bi. The (self-reported) numbers of LGBT people keep rising (to the point where in some surveys 40% of the youngest adult generation in Amsterdam are LGBT now, with particular emphasis on the B, particularly among women apparently) and most of that is due to increased social tolerance.
Still depends if I like the other suitor at least somewhat, but I tend to agree. However for a poly relationship all parties have to like/love one another it won’t work if you’re just crushing on the same guy but don’t like the other fellow crushing on your crush too.
The Myrmidon used to have a particularly promising potential gay poly relationship in its noble branch.
No one will romance me 
Why ??
Among some of the other concerns people have mentioned here, I would be worried about what kind of MC I need to be in order to “win.” Do I always need to agree with RO? Always do what they like?
Obviously not every MC is suited to every RO, but there should be room for disagreement and differences. I don’t like games where I have to be a very certain personality to be liked by certain characters (ROs or friends).
I might be more open to this kind of love triangle if MC and RO have known each other longer (maybe there are some unspoken feelings on both sides–though the MC should have the option to decide if this is in fact the case), then a new person shows up who changes the dynamic and stakes. Will MC finally make a move/confess their feelings?
I think it could be awesome, I would love to play a game in which I am not in the middle of the love triangle but fighting for the love of my life.
I think to make this work, there should be an obvious intense connection between the MC and the RO, something that you can’t simply turn around and ignore. This way, I think it would be very interesting and full of angst.
I also think that to make this properly, the love triangle should be the main focus of the game, otherwise it would be very easy to ignore and wouldn’t be, in my opinion, developed in enough depth to be worth the suffering.
I personally if there is a rival in a game My only feeling is DESTROYING HIS LIFE IN THE MOST MISERABLE WAY UNTIL SUICIDE. if that’s not possible Destroy the Ro and make him die and be misserable.
If not make both together and miserable
If all will be goodie goodie soap unicorns I probably wouldn’t even trying ro that person anymore. I role play evil and Sugary rainbowz is not something I crave for.
As writer however I have a only open poli game relationship. One romance will negate anything that won be open. Other will kill absolutely any other possible rival for you. Also I have several types of only hang out or only friends for sex. To a friendship that could end in a night of sex or totally never more than frienzoned.
I have very much fun planning how My RO Necromancer Alex will planning killing everything in his her way for you. Sometimes in very fun noir comedy moments.
My main goal is realistic and organic way to present relationship. No relationship metters or need of stats to romance anyone. Just your actions and how you say it determines the outcomes.
That’s very… uhhh harsh
My role playing character Mara is pure evil or A mix between chaotic evil and nwutral evil. Is a bard poisoner No Mary Sue lol. If mara wants someone she Wants him for her only and any other has to die.