Peel and Stick Vinyl tiles
There are two issues with particle board: One is that the particles aren't glued that well to each other. Put a stick tile on it, and after a while you get a sticky tile with crumbs of particle board.
The second issue is taht with wood in general the wood soaks the glue off the tile, and the tile becomes new toy for the dog.
The second one can be cured with a good primer. The trafficmaster directions say taht this is how you can use it with plywood. I suspect it would also work with good quality OSB subfloor too, but haven't tried it.
I thought of using a oil base paint (to not dissolve the glue in the particle board). But particle board just drinks up paint -- Instead of 400 square feet per gallon, you get about 100, and the house will smell of paint for weeks after.
You MIGHT be able to get away using a self leveling compound. Better would be WEST epoxy system. The idea here is that you get the surface to stick to itself better, and not slurp up the glue. Both of these make changing your mind later difficult. I was in a similar situation a while ago. I found no good news that I wanted to bet a floor on. I chose to use laminate.
On the ohter hand: Traffic Master is cheap. It may only work for 3-4 years, but at a buck a square foot, that may be enough.