How can I waterproof walls that are not shower or basement walls?
Remember that concrete is porous so even if you have a floor drain some of the moisture will seep into the concrete. Seal the floor with a penetrating sealer or an epoxy floor paint. Maybe even an elastomeric membrane you paint on before applying tile on concrete slab floors. RedGuard is one type of product. 

Your best solution would be to build the entire room like a shower like you mentioned. Moisture barrier on walls that extends a few inches on the floor and is sealed to it. Cement board or hardibacker covered in tiles. If you look around you can find cheap tiles. There are tiles stores around me in industrial areas that advertise $1/sq ft tiles. Home Depot has a 4x4" tile going for $0.16 each.

If the tiles are too much money... 

If appearance isn't a concern maybe you can just paint over cementboard walls with the elastometric membrane?

Also Quikrete has a waterproof cement product called QuickWall Surface Bonding Cement. It's main purpose was to parge over dry stacked concrete block walls but it's also used for cisterns. You spread it on with a trowel like stucco 1/8" thick. At 50 sq ft per bag it comes out to about $0.32/sqft.

I've used it and it really is waterproof. I painted over it with DryLock waterproof paint for a nicer finish. I spoke with Quikrete and they said the DryLock wasn't necessary but already had it and I wanted a smoother surface on the wall. You could probably just use a regular, mildew resistant, glossy paint instead. Call Quikrete and see what they have to say because it's been a while since I used it. You'll want to let it cure a bit before

I mixed it up I think 1/2 bag at a time in a 5 gallon bucket with their acrylic fortifier using a drill and paddle mixer. Spread it on using a cement trowel.