Mortgage
A mortgage lends money against a piece of real estate. The borrower repays it with interest over years, and the lender can claim the property after a default. Gross rent multiplier ignores financing completely. It measures price against rent whether the buyer pays cash or borrows most of the price.
Financing is where GRM stops being enough. On the $500,000 example, a $375,000 mortgage at 7.5% over 30 years costs about $31,500 a year, more than the property's net operating income of about $29,200. The same GRM of 10.4 is fine for a cash buyer and negative cash flow for a financed one.
That is why financed investors usually need a lower GRM than cash buyers to reach the same result. Under this site's default assumptions, a financed buyer with 25% down at 7.5% breaks even near a GRM of 9.7. A lower rate raises that break-even multiplier, and a higher rate lowers it.
Further reading: Mortgage on Wikipedia.