During the initial fight, Artemis/Hunter was probably to pissed off to think clearly and use their lighter.
Correct; they really don't know what they are doing. Remember, in the bit posted above, Artemis was also chanting/posing/etc. Maybe they thought some magic might flare up the lighter and engulf the Wendigo...
And as for the chanting, some legends hold that it is a cannibal spirit which takes over a human...aka...a possession and turns someone into a Wendigo (this is not the route Sashira went with). As Artemis and Hunter don't know better, essentially performing an exorcism makes sense depending on the info they dug up.
Artemis and Hunter definitely are beginning monster hunters. Will they make mistakes? Certainly, and in practice this would kill a lot of monster hunters until they find out what works and doesn't work. Still, that is certainly a couple steps above everyone else around them who would laugh at the existence of monsters.
Of course, if there is a monster hunter secret society, then Artemis and Hunter would be prime candidates for them.