that last kick from Batman was awfully powerful for someone with no "Super powers"
Also Batman catching the shield, applying explosive gel and sending it back?
Batman deflecting straight on punches from Cap might break bones, certainly trying to deflect that Shield thrown at full strength would disable him from continuing to fight.
Batman's advantage would have to be out of line of sight attacks and not a straight up fist fight. Because in a straight up fist fight, Batman loses everytime. It's not even a fatigue thing. Cap punches with the force of 5 Tyson's. Batman's armor can dampen it as much as it wants, but he is still just human. A full force punch would probably break something and knock him out cold, blocked or not. Cap can react fast enough to dodge bullets, so I doubt Bats would ever land a clean punch in a straight fight, and his shield is practically indestructible and absorbs all force/kinetic energy.
So I call bullshit. Bats wold have been downed after the first exchange in that fight. and certainly after the shield hit him in the back of the head.
I'm sure there is a way Batman could win, but that fight in the video wasn't it.