There are objectively favorable conditions in the experiment in the video but there are no objectively favorable conditions in flipping a coin. It is 50/50 in the long run. But even if you ASSUME (although why would anyone assume that anything will go to infinity?) that the probability of tossing your coin skewed towards the favorable side, you use only two outcomes in your assumption - increase and decrease in value. You don't factor in other outcomes, such as those that could cause Bitcoin to cease to exist.
It's about EV. The favorable condition in the coin flipping game is when you pay $10 if you lose and earn
more than $10 when you win, which is the game proposed later in the video and gives you a positive EV.
In terms of asymptotics there are only two possible outcomes for the BTC price, regardless of the factors that may drive it - it's either going to infinity or to zero.
By going to infinity I mean there is no positive real number x such that BTCUSD will never exceed x.
If it's neither going to infinity nor to zero, that means its USD price is going to range between some x and y forever, which would effectively be a peg against the USD. How could a finite supply asset be pegged against a fiat shipcoin forever? The USD would have to have a finite supply too, because the convertibility would have to work in both directions (otherwise there would be no market and therefore no valuation). The USD would have to be backed by Bitcoin. Not something I see happening in my wildest dreams, but even in that case, the purchasing power of BTC (but not its USD price) would go to infinity.