"Rent" as a word here refers to "regular payments to use something", of which rents for housing are only one specific example. For example, printer manufacturers who force you to buy only their (incredibly expensive) ink, or razor makers who benefit from regular purchases of blades.
The term "rent-seeking" has an even broader scope:
https://en.wikipedia.org/wiki/Rent-seeking
> Rent-seeking is the effort to increase one's share of existing wealth without creating new wealth. Rent-seeking results in reduced economic efficiency through misallocation of resources, reduced wealth-creation, lost government revenue, heightened income inequality, and potential national decline.
In the case of the razor manufacturers they can at least claim that it's completely natural (I'm not sure how far they go to prevent cheaper blades to be made available for their particular razors?), but often the regular payments are artificially forced through contract clauses, laws, patents, copyright (I guess?), and/or through technical means. In the case of printer manufacturers, they started adding electronics to the cartridges that force you to buy only cartridges made by that specific printer manufacturer.
Basically, it is a goal of many businesses to end up as a "rent-seeker". Have a wall that keeps out competition and a large number of customers forced to regularly buy from you ("regularly" is key, for constant predictable cash-flow and an easy life free of competitive pressure and uncertainty - for the rent-seeker).