I found out how to play it and I figured out why you can win without the store.
Actually by not knowing the store you were even at an advantage, which I guess might be technically some issue with the game's balancing.
When I bought stuff from the store I actually lost before Day 3 or even lost on Day 1. When I almost never bought anything and just bought something at the very end just in case, I was able to win the game. I think that might be a problem with the game's balancing because it's too emphasized on manpower, and buying stuff from the store uses lots of manpower fast.
Making the right decisions on the folder outweighs even using the store at all! You not even knowing the store was there and you won anyway means there might be some problem with the balancing of the game or something.