And how much battery life do you think that would possible get? An hour or two?
For regular use, it'd be pretty much the same as any phone. Extra ram, gpu, and SSD actually take strain off CPU.
For gaming, it would depend on the game. Typically mobile gaming either requires a huge battery or has a short battery life. So for gaming, yeah that's an issue. Fortunately we are just now seeing the benefits of new battery tech - for example the mixed lithium the s8 uses, has a longer life.
Most people bus stop gaming, don't game for that long, but I reckon you could get 2-3 hours, max 3d graphics, if you really tried, without making it switch thick. Look at how thin the s8+ is. 3500 mah. You could make this phone a tad thicker and have probably 4500-5000 mah. Which on a smaller screen would do you pretty well.
Clearly an entertainment smartphone is going to be thicker than a regular one, as its built for power. Like slimline versus laptop.
I think the old edge tablet by razer did less hours gaming than what you could make this do nowadays with modern tech. I think users would find that satisfying. Especially considering not all games push that hard.
Practically its a concern (well, to be fair, not really much more than any mobile device when rendering 3d - you get the same quick drain on any device to some degree, but most devices aren't built for the purpose, so they perform poorly and don't have the juice), but the biggest concern (given the advances in battery tech) when making a mobile gaming device of this style would be heat.
Reckon liquid cooling might be the ticket. They have that in some tablets now. It'd probably have to be fanless, so your heat design would be the real design challenge - make sure it doesn't turn into a hot coal while your playing it.