Watch it again, Carmouche didn't even come close to sinking in that sub - Rousey did everything in the correct order to get out of it without being in danger. If you don't believe me, watch the Gracie breakdown of the fight, they say the same thing.
Rousey isn't used to the fence yet, she let Carmouche walk up the wall to get out of her head and shoulders hold. I'm not sure that Kyra is any more used to the wall than Rousey is, so I'm not sure that helps much.
In terms of submission skills, Kyra is obviously a lot better than Rousey. In terms of throws and takedowns, Rousey is obviously a lot better than Kyra. In terms of everything else involved in MMA, its hard to say. Both reportedly have almost no striking worth speaking of. Basically, if Royce is sure Kyra can sub Rousey, he might be trying to convince her to give it a go. A MMA fight against Rousey is in fact a grappling match, since Rousey has almost non-existent striking.
My suspicion is that under MMA rules, Rousey wins simply because of size.