How do I apply tile to a small wood platform?
The reason for cement board is to give a good adhesion surface and to increase stability. When a floor flexes from the weight of people walking, or from movement of the house, grout and even the tiles themselves can crack. For a temporary platform intended for a cat box, you're not looking at a lot of weight causing flexing, so I doubt there'd be much cracking. For adhesion, just check the product you're using to make sure it will adhere to wood, but I believe most thin sets and especially any mastic will work without issue.