Can I install Kerdi board just on the walls of my shower and use a PVC membrane on the floor?
That makes sense the installation video from Oatey says "wateproof drywall or cement board"  but your kerdi board is waterproof too, so it's equivalent.

Be sure not to screw through the shower liner--if you need to screw low on the Kerdi board put a dwang (cross-block) in above the liner and screw to that.