Even if they're not doing the animation, they should be doing the damage. The running animation is annoying to be sure. Pay attention and see if the mole rats are actually dying. If not then you probably have a bug.
Also, what level are your guys. If you're putting people under level 40 in a level 3 room, the mole rats will do far too much damage and have too many hp for your guys to fight. The room level determines their toughness and damage.
I have no trouble dealing with molerats with dwellers in size three rooms that are well bellow lvl 40 (in their 20s). But I have constructed my base so that only the bottom three rooms ever get molerat attacks by keeping all Elevators on the far right and far left sides of my vault (Elevators are immune to room events). This leaves one elevator that goes no where on the first floor right after the vault door but its not problem. Having only one elevator connecting the 1st and 2nd floors on the far right but the rest of the floors have 2 is also not a problem.
My current population is 150ish and now growing slowly so I can take time to increase special and their lvls and I sent out two high lvl dwellers on wasteland runs for equipment. So far because none of my upper floors have any room touching dirt molerats are a very rare and not very tough.