Two out-of-the-blue headcanons as to why Stan owns all these board games:
1. They’re actually Ford’s from forever ago, hence why the boxes look pretty beat up, and he and McGucket would play them all the time together when they weren’t working on the portal. (I looked it up and nearly all the games these are based off of existed back in the 70s/80s.)
2. When Stan found out that Dipper and Mabel were coming to stay for the summer he figured that he had to get something to keep them “preoccupied and out of his hair”, so he picked them up for like a buck each at some random family’s yard sale.