Relating content types to be used in Views filters
Nikit's response about using Relationships in the view is correct, but it's not clear you've have already set up the correct 'node references' between Games and Developers. 

So, rather than maintain your own lists of Developers for a Game, you need to use the References module to add a field that allows 'connections' between these content types. You might also want the Corresponding node references module to auto-update the reference field on a Developer when you edit a Game, and vice versa.

From here you can properly relate Games and Developers, so Views can use these relationships and allow you access the associated Games from your Developers view.