DEEPSPACE DJ is a passion project by someone that chooses, willingly, to go by 'Thighs', that's a red flag if ever I've seen one.
In short, it's an incremental game that drapes itself in the trappings of science-fiction and stews itself in the flavour of being a disc jockey in deep space.
This is a good question, and I'm annoyed that I have to ask you for permissions myself.
It's probably for the best that I do have to ask, all the same.
Basically, when the game wants to save (a variety of ways that do this are implemented, including trying to save if you close the window by mistake), it tries to convert the pertinent information of your game into a single, long, string using JSON; this string is then parsed and re-applied when loading the window or clicking 'Load', in theory.
Without cookies, this ceases to function, as the save data needs to exist in localStorage. I would have it be exportable solely, for people more keen on privacy/the sanctity of their browser, but this method covers our bases for accidental closure and I'm not keen to waste your precious time.
I'd be more than happy to use an alternative, but I'm not great at HTML, JavaScript, or CSS. I just want to make the game as best I can.