Just wanted to report my experience with an Exxon Mobil card in case anyone else was on the fence about trying it.
The Gyft app has a way to enter it but the clerks have no idea what to do with that. They said they've never seen anything like it before and had no way to input gift card numbers manually. They said everyone else swipes their card. Of course this could just be employee error, as always.
Only a $5 risk and the seller warned on the site that he didn't know if these would be taken. I will likely try again at another location.