The backboxes on modern sterns are 28" wide but many older games have 30" wide backboxes. That would mean you need at least a 25' long wall for 10 pins. I would make it a bit longer if you want space between heads and more room to reduce Jazz Hands and also for working on them.
I think the typical pin is just under 5' long but you need space for the person to stand and space behind the player for people to pass by. Assuming 3' for each player on each side that would leave you with about 2' for people to walk between.
Assuming the doors are in the center of the short walls I would go with at least a 20'.
also, don't forget that drywall and trim take up a few inches of space at each wall.
So, my recommendation is at least a 20'x30' room.