They obviously forgot to have this checked by their legal department. First, qualified stay is capitalized so you expect this to be defined in their terms and conditions. But it's actually misspelled, what they mean is Qualifying Stay. Second, and more importantly, it's highly contradictory. "Qualifying Stay only" rules out stays booked through an OTA. But the examples given of "Qualified (sic!) Stays" then include it.

While you may get that interpreted to your favor in a court of law (especially in a consumer-friendly jurisdiction), I think the hotel and IHG may very well say no. If you're clued up on IHG member terms and such, you should be able to recognize this to be the mistake that it is. We can even speculate this is documented correctly internally and erroneous on the web site only.

In practice, I'd very much consider this an YMMV sort of situation.