It’s not untrue that it boils off, but dilution is the bigger factor by a wide margin. When I use wine to deglaze, it will be 100ml. That is then turned into 2 or 3 liters of sauce, so a dilution of 1:20, 1:30. Or, expressed in percentages, 3-5% of the sauce would be wine if none of it evaporated - 14% alcohol would be reduced to less than 0.5% just by dilution.
To get a similar reduction from evaporation, you’d need to boil off 95% of the alcohol, assuming none of the water is also evaporated, which it will at the temperature of deglazing. I don’t know the exact ratios here, but even a 75% net alcohol evaporation (which I think is generous) would leave you with a 3.5% alcohol (light beer) before dilution.
Edit: the table he shows has 95% actual alcohol loss for a 2.5 hours simmer, but every other method (where you’d “burn it off”) is below 25%, so that’s definitely a noticeble amount of alcohol left in, especially when you start with something like a brandy.