I ran with this when I saw an article suggesting the video shows he paid, but in the end I took down my support of that view.
There are things you can deduce from the video that works each way.
In Support of Purchase:
Brown has a number of products he seems to have taken to the counter and the exchange with the clerk, and his other movements and behaviors, come across as very natural; he's not being forceful and he's not attempting to be sneaky. There's even some movements that indicate he left some products behind as though he couldn't afford them all. Then, when the clerk comes around and goes past him, there's no sign of hostility or strange behavior by either person.
Then there's a couple other things not directly related to the longer video. If the clerk went up there with the intent to stop Brown, well... that's just an incredibly stupid decision. Brown is twice his size. How exactly did the clerk expect to stop him? Lastly, the clerk never called the cops to report a robbery. The call was made by another customer and there's no telling what that customer saw; if they only saw altercation at the door it'd be logical to assume a robbery, but perhaps not factual.
In Support of Robbery:
The final altercation would suggest a robbery, though it remains possible there were simply words exchanged that offended Brown, or some other cause for it. Then the store hasn't seemed to dispute the fact there was a robbery, so there probably was one.