A rookie mistake, we've all made them. Now that you have this one under your belt, you are no longer a rookie, so don't do it again! (Ahem!)
Absolutely no doubt the electric element is burned out. They only last seconds if there's no water in the tank. And absolutely you have to purge ALL the air out by running a hot water faucet as long as any air comes out. The high limit switches are safety devices that prevent your water heater from turning into an exploding boiler. Google "exploding boiler + 1930s" for some real horror stories. A tiny boiler like you have would probably only level your trailer along with the ones on either side of it in the campground.
In any case, unless you managed to melt the bottom of the tank off -- which should show up very quickly when you turn on the water, you are probably ok.