Pretty sure he meant that a simplified return sequence, where incrementally increasing losses are merged with their subsequent win, results in a sequence of wins followed by a huge loss when no more bets are afforded. OTOH he causes confusion by bringing in e.g. mean reversion which is a statistical tendency. In the long run we're all with scaling bets/unhedged exposure >= 1 either broke by some outsized negative return, or dead, whichever happens first, and that is not related to martingale trading. With martingales being broke tends to happen far sooner though, especially since financial returns are neither normal nor IID and not as kind as betting on fair coin flips.
Value investor here... Both my wife and I try not to average down. We usually set a limit ($) on how much of any one stock we own...Mutual funds and ETFs may be different. Our only two stocks above the limit are Teledyne (TDY) and Apple (AAPL...200 shares). We needed 100 shares to do covered calls on them over the years...
Martingale only works in Roulette if your bankroll is much bigger than the casinos. Average Joe with 100K net worth or 1M net worth cannot win against a casino with $100milllion reserves using martingale. However a multi billionaire could bankrupt a $100milllion casino. So a casino ideally does not want any limit for the Average Joe. Take them to the cleaners. But the risk is the Average Joe might cheat and collude with a dealer so they set a max bet limit to something like $1000 or below. You still need something like a $1M limit for billionaires. And only have your most trusted people operating those high stake tables.
I remember right before the 2016 election I kept doubling & tripling down on worthless options on WFC, which had dropped a lot based on being sued for create phantom accounts. I think I had 60 contracts of a 10% out of the money calls, it had mo ask and a bid of $0.01. Right after the election it went up 10-15% in next 3 days. I think my average cost was $0.10 and it eventually went to $3+ but I sold all of it at $1. It went from zero to $3 in 3 days. I knew that was just Trump & the GOP winning across the board. So pure luck.