that's not entirely true. they will need to have higher res textures and images, and then actually load those into the game to get the true higher res.
but at the same time, that won't be too much extra work so i see what you mean.
Screen resolution has zero to do with texture resolution. You can (and I have) run n64 games with 32x32 textures at 1920x1080 and it's still a huge improvement in image quality overall. In either case, most cross platform games also target PCs and tend to already have those higher res textures and flexibility in the engine.
Plus, more processing power enables them to increase Antialiasing, shadow precision, number of light sources, particle density, physics precision, shader precision/complexity, texture filtering, draw distance/LOD, tessellation, etc - basically anything procedural, with the only real work being inputting larger values and optimizing for the particular power of the system at hand.
It's not particularly difficult in any way, and it's fundamentally the same thing we've been doing for years on our older PC games as we upgrade through the years, and it's all done by the user. Just basically turn the knobs up...any PC gamer fundamentally understands this.
This is why the whole "devs wont be able to afford the next gen" argument is bunk. There's plenty of very easy ways to soak up that power and put it to good use with very, very little work.