Under german law, it would be anyone officially acting as security on that property. (It does not have to be a professional security, it can be anyone from staff filling in that role).

The police does not want to be called, for every bouncer action.

It can get into a grey area, if violence will happen, the security may not simply beat someone out - but grabbing and forcefully moving or carrying out is legal. But if there is serious resistance and the security unable to handle it in a nonescalating way, then they would need to call the police. But usually, the bouncers would just get brutal, then. Attacking security gives them some freedom to act.

If other people are endangered by someone, very different scenario, anyone can (and must if possible) stop violence.

Source: short stunt as a professional security

In Canada, in our Criminal Code,if you order someone to leave the inside of your home, and they refuse / do not?

They have committed assault against you.

This serves two purposes. The first is, a crime has been committed. The second is, you may now defend yourself.

I'm sure there is something similar in common law for other buildings. EG control of a space.

(I know nothing of this incident, just speaking generically.)