Why not test that mat on a computer to see if it can be detected? It's better if you can do it on PC than PS3, because it's easy to download the emulators for DDR and play it that way.
Foldable mats are junk. They stop working for all sorts of reasons. I think it's because there are wires that flex all the time and end up disconnecting or snapping etc. You might have a dud of a mat.
A minor exception I ran into, is that there are versions where they put interlocking foam inside the mat. Those lasted longer and didn't slide around etc. If you end up with a folding mat that works, I'd definitely suggest mounting it permanently to foam tiles. It'll work better, slide less and last longer. Best you can buy without going all out on metal mats.
This is what I bought many years ago for my PS2.
And I'm curious whether you can attempt to play DDR on a PS2 instead of a PS3? The mats might be cheaper.