it's meant to allow you to use your preferred peripherals. there is a keyboard remapping and gamepad remapping menu in the pause menu (can open by pressing ESC) under settings and then in the controls section. is it having problems recognizing your pad or accessing the menu?
i haven't been able to put together a full mechanic-overview-tutorial for the game yet, as the project is very much still in progress. the opening "dont you remember" scenario is a sort of challenge gauntlet that rapidly builds in difficulty. you can exit it by taking the option "please let it stop" after losing all your extra lives to take a reset back to the actual main area of the game, where the game gets a little more sandboxy and gives some space to play with mechanics. You can revisit it later by talking to the Miko and asking her "don't you remember?".
beyond the guantlets there is not as much linear progress to the game, as it is in a sandbox state, essentially a big tutorial play area.
i'm sorry for the frustration with the poor documentation, it's been hard to stay on top of everything and i am failing in that regard.