Did I appear desperate?

This has trouble written all over it. There is no way you should be thinking of calling him outside of the gym if you both are married. Maybe one of your spouses wouldn't mind it, but I doubt both would see it this way. And that means someone is going to get hurt. Stay friends; but keep it in the gym. And keep it professional; unless you want trouble in your marriage.

Harmless flirting is one thing, and intention is everything, flirting doesn't mean he wants to cheat on his wife.

Its hard to say, I can only hope you made it a point to make sure he knew that you gave him your number as a friend who would want to do something outside the gym rather then as a someone looking for something more...

He seemed interested in what? Cheating on his wife, or just hanging out with you? Unless he mentioned he was looking for somebody on the side, it seems that it was a quick move as many married guys might also flirt. But as they say, they won't go beyond that.

Are you sure you gave him your number or was it a recipe for disaster? Just checking...

I'm all for some innocent flirting, but I'd say your move was a bit much.