It stems from Han Hoppe's insights about incentives and time preferences in various political systems. Monarchs are conceptually simplified to owners of their countries who will pass them on to their heirs, while elected officials are more akin to renters who have no long term stake in the value of the country they're ruling.

Owners tend to protect and enhance the value of their properties, while renters tend to extract what value they can before they relinquish control.

What generally gets lost is that they aren't "Monarchists" per se, but rather are pointing out that democracy is not as clear of an improvement as people assume.