Option 1: Upgrade the screen and put in an M1. It will ding battery life a bit, but as long as they can keep it above 4 hours for gaming, it should be fine. I know the M3 is much more of a gaming chip, but you can get this in now to make steps.
In 3 months the M3 goes into the iPad Pro as a “proper” gaming platform. Ditto v2 of the Vision as a gaming platform. For travel gaming though, an M1 6 inch is a perfect size.
With those upgrades, you have an intro competitor to the Switch or Steam Deck, if you can get the decent game studios onboard. Playstation Remote Play already shows this is viable, but the mini needs a better screen for that to work. Support for Spatial Audio on headphones is necessary.
This feels more like a Steve play - ambitious reach into a new(er) market. I have to question the state of AAA gaming at the moment, so maybe more studios drop down to AA at a $15-20 price point. Challenge here is re-educating people that a last gen game is still quality (with Sony and Nintendo rocking the back catalogs on way old platforms, I think its there). Go whole hog crazy and buy up a studio - they have the cash.
Option 2: minor spec bump (A16a, upgraded single camera), rotate to minimise jelly and keep the price seriously low. Casual reading, browsing, entertainment. I have a feeling this is the direction Tim will go.