The most popular FPS of 2037 will be a fingerguns RPG hybrid where characters' adherence to the kayfabe of imaginary Uzis, grenades, pump-action shotguns and headshots depends on your relationship with them. We can't predict the direction the genre will go on, which weird addition or experiment will catch on then be repeated and iterated upon for years, compounding with other oddities to make something bizarre.
For now, in 2015, perhaps the answer is a pogo stick. That's what Pongo [official site] went for. It's out now, so you can judge for yourself whether it's a vision of things to come.
Pongo's an single-player first-person shoot-o-platformer where you have a pogo stick. There's probably a good reason for that. On it, you'll super-bounce around floating islands, zapping enemies and solving puzzles. Pongo did have a demo when it initially launched at the end of April, but that's vanished now the game has arrived on Steam. That's both a shame and a mistake.
It's also a shame that it's so unattractive - I often dig untextured low-poly art styles, but they need to be backed by strong art direction. See Lovely Planet, which looks similar in ways but much better.
Anywho, if you're curious, Pongo is on Steam for Windows at £5.59.