Wondering if it was possible to transfer any purchases made through app stores such as iTunes or the Google Play Store to my laptop so I can play it through there??
Like I have several games purchased through the App Store (or the Google Play Store when I had an android) and I want to be able to read it on a bigger screen when I have the time 
If you have the receipts from the app store, you can send them into CoG and have them unlock the games here and linked to your account here, then you can use a browser to play them.
The mail is:
support
@
choiceofgames
.com
(go to put it on individual line so it won’t get spammed by bots)
Can the same be done if the game is downloaded on Steam?
Yes; I believe it will auto-synch now if you link your steam account.
How can I link it?
If you use the same email for Steam and CoG then go to the site and ‘my account’ and restore purchases from there, you can do it for individual apps on the omnibuses as well
Thank you for answering the question for me. 