In this simulation, the amount of money you have does not affect how much you have to give away per round (until you get to $0, in which case you give away nothing) or how much you will get per round (until some people get to $0, in which case the money you get is less on average). So in most cases, with whatever you have, you are expected to see a gain distribution with zero mean. Since it's not a self correcting process other than at the $0 end, it's not surprising to see (1) a snapshot with uneven distribution, (2) no one dropping out permanently.

Actually I don't know what is the point they are trying to make with this video. There is neither anything surprising in the general sense nor a solid statement about what is specifically seen.