I wouldn't be so sure, many of the big A list names are owned by the big 3 companies.
I for instance I have a PS4 pro and a Switch, I want to be able to play Marino etc plus gran turismo, uncharted etc. do I really want to buy a third device to play another group of exclusives on?
I think Apple know this isn't their market and it's not one they would be guaranteed to succeed in.
Plus this device would be nothing like an Apple TV. If a PS4 Pro is $560 then with the Apple tax a comparative device would probably be close to $800. I'm not sure your typical gamer is willing to pay that and a casual gaming type certainly won't.
This would be a short to medium term strategy.
From casual online searches, it looks like revenue from mobile gaming is projected to, or already has, overtaken console and PC gaming, individually. As smartphones get more and more capable, combined with their being right there with you at all times, I believe mobile gaming will grow to become larger than consoles and PC gaming, combined. While there are and will always be hard core gamers, they are the connoisseurs of game media. I agree Apple will not easily attract people who enjoy not only the gameplay, but the ability to fine tune frame rate and other specs to levels I, as a mundane, cannot appreciate or comprehend. And Apple may not be able to steal Baby Boomers and Gen X'ers who grew up on certain game series.
But, my son is in the fifth grade. He knows Mario, he knows Zelda, he knows Master Chief, but he's not obsessed with any series or games having great specs. And he's probably already played more mobile gaming than on any console. In 3 to 5 years, that may change.
I think there is an abundance of excellent independent game companies out there that would do a fantastic job of creating games for Apple for recognition on their App Show and for a chance at some of that $1B. Apple is in the unique position where someone in their ecosystem could download a game for the Mac and have a copy for their setbox, tablet and smartphone.
No other company can do this and I believe it would be a game changer and allow Apple to dominate not just mobile gaming, but gaming in general.