Depends on what you mean by "rent seeking."

Liberal economists use this term the most, they usually mean large companies trying to get goodies from the state. Lefty ones tend to mean something like "profiteering."

X-as-a-service businesses models aren't exactly new in intellectual property. The patent/copyright systems explicitly assume licensing and royalties. But, I agree that subscriptions are pretty new in consumer-land.

But we need a different term rent seeking already has competing usages.

Rent seeking [0] typically means exploiting a captive market without providing value. I don’t think that fits either of your definitions. The key piece is they basically squeeze without proving value. So buying IP and then upping the rent fits that.

[0] https://en.wikipedia.org/wiki/Rent-seeking

>they usually mean large companies trying to get goodies from the state

I think here you might be thinking of Regulatory Capture.

https://en.wikipedia.org/wiki/Regulatory_capture

Property(intellectual and otherwise) enforcement _is_ a goody from the state, by the by

> Liberal economists use this term the most, they usually mean large companies trying to get goodies from the state.

No, they don’t. That is neither a correct nor common use of the term.