Custom Entity - use taxonomy fields in views
You didn't say that you wanted to do this programmatically, so I'll give you the answer for doing it in the UI. Since you have defined the field game_category as an entity_reference, you can add a relationship in your view to Taxonomy. See Add a relationship to a view for an example.

Then, any field in Taxonomy will be available in your view, including the name. Since this is built into the Views UI by default, you do not need any of your getViewsData() custom code.