Sticking strictly to the OP's points - from the video, it is quite clear that 'Tommy Robinson' is at least as willing to fight as his provocateurs. He could have walked back into the restaurant and asked for the police to be called. Instead, he advanced, throwing a punch as he did so.
There is no evidence whatsoever of the political leanings of the group of men involved.
'Tommy Robinson' is called a thug because he is a thug, but his own admission, and by his police record.
Do I condone this violence? Not in the least.
Do I think the OP's protest that 'Tommy Robinson' is described as a thug is of the mark? Absolutely.
'Tommy Robinson' is a thug, and could have avoided this trouble very easily by walking back into the restaurant and asking for the police to be called. He waded in throwing punches because that is what thugs do - and he is a thug.