According to Dr Erskine, he heals at 4x the rate of any normal human, which is pretty superhuman.
The movie shows him, among other things, grabbing full grown men, at least 200lbs with gear, and with one hand tossing them around like inflatable sex dolls. He pulls the bonds holding Bucky to the table apart like they are paper.
The movie has made a character that's a little below Spiderman in strength and a little below Wolverine in healing, but he's plenty superpowered.
I don't have a problem with that, but he's obviously got more than the stats from the Marvel Super Heroes RPG.