I think the main difference between Take Two and Nintendo is that Nintendo also sells consoles so they are not exactly on the same level.
There are 3 large game companies: Take Two, Activision, and EA. I have positions in Take Two and Activision but I would also suggest that you do your own due diligence.
I am not interested in mobile gaming specifically but I can hint to Sea Limited which is active in mobile gaming in South East Asia, but they are not a pure play gaming company as they also operate in e-commerce sector. I guess they would focus on e-commerce more in following years when they become profitable in that sector. It is also easy to scale a e-commerce business than a gaming company I guess.
Developing hit mobile games are relatively easier which enables many small or new companies to develop git games. So there might not be large dominating companies in this sector compared to computer/console gaming. Investing in game engines can be a good approach as almost all mobile games use same couple of game engines such as Unity or Unreal Engine.