Well, it seems to be working now... and it seems like the issue was on my side.
The addition of the pre-launch Input Selector dialog made me look into the issue in more detail and try all the keys again. And, as it turns out, i didn't try all of them before. Several of them worked, and i was even able to enter a mission by pressing Q twice. Still, the WASD input didn't work a single bit. It felt... stuck. As if some gamepad was connected and the stick on it was pulled fully to the side.
Which made me check my gamepads(or the lack thereof) again using that html5gamepad site. Turns out there were two virtual gamepads, which were VJoy's fault, and they were outputting NaN(is that even legal?!) on most of their axes.
I went to the Device Manager and shut them down. And yep, the game is now fully playable.
Long story short, i am not smart.
Sorry for wasting your time like that. I'll go ahead and finally try the game out properly, probably tomorrow. Though i did play it for like 5 minutes today after i figured out my input issues and, unsurprisingly, it looks and feels really good.
I think you should keep the pre-launch Input Selector enabled, though. It's quite the useful thing, allowing players to tune the settings(input, graphics quality, screen resolution) through a reliable UI.
Yeah... sorry again. I should've handled this better