Is the author accounting for the equity built up? Cash has to go out whether it’s a mortgage or rent. With a mortgage you are building equity. This changes the true math when you sell (leaving aside your ability to now get a HELOC).

He's saying - and rightly so - that outflow towards rent can be significantly less than outflow towards real property equity given the structure of a traditional mortgage + maintenance burden. And with (a large amount of) financial discipline that delta can result in substantial increase in wealth at the end of the day.

Yes the author is accounting for the equity buildup. They only count the interest part of the mortgage repayments as an expense. Any principal repayments are neutral.