Almost every person who plays the game will see their money decay towards zero as time goes to infinity.

Knowing the time scale is very important.

but, since it is somewhat like a random walk, isn't it guaranteed that if you go on for infinitely many tosses, at some point you will be very rich?

[1] https://math.stackexchange.com/a/493446

if true, an interesting question is - on average - how many tosses are needed for you to reach some arbitrary value (e.g. $1M)?

It's exactly like a random walk... with downward drift. If you take the log of the wealth, the steps are: log(1.5) = 0.18, log(0.6) = -0.22. So at each step, there's a 50% chance you go up 0.18, and a 50% chance you go down 0.22.

Random walks with downward drift don't inevitably go up arbitrarily high like ones without drift.

The percentage of losers would increase slowly and linearly from 50%.