I'm not sure about it - but they say they did. In their recent FMS3 white paper on page 8 there's a reference to "the Adobe patented, RTMP over Transmission Control Protocol". I'm not sure if this was common knowledge but as far as I remember there was no known patent in existence around RTMP - but it certainly looks like there is now. A quick Google patent search brough up this result.
While RTMP has not been patented explicitly in this patent, something that sounds even wider reaching has (at least to my limited experience), namely a "Method and system for facilitating communications between an interactive multimedia client and an interactive multimedia communication server".

While I don't know if this particular patent is the one cited in the white paper but it was the only one I could find that appears applicable. It is US patent number 7246356, filed on Jan 29, 2003 (that's not too long after FCS was released and way before FMS2) and issued on Jul 17, 2007.
The inventors list is a who's who of Flash and FMS and includes Slavik Lozben, Pritham Shetty, Jonathan Gay, Stephen Cheng and Bradley Edelman.

I'm not sure what implications (if any) this patent may have for the likes of Red5, Wowza and other RTMP servers but it certainly appears that Adobe wants to protect their intellectual property at least on paper and 'just in case'.

I say this because the patent has been granted a while ago and of course no legal action of any kind (that I know of) has been taken against anyone who has implemented the RTMP protocol, and I doubt we will see this happen either. But stating quite openly the fact that RTMP is patented is a first a far as I remember. Patents are of course a daily occurrence at Adobe - the Google Patent search is limited to 100 results and a search for Adobe as assignee brings up 100 matches, suggesting that there are way more.
What do you think to this? Should Adobe draw a line somewhere on how it 'allows' others to implement RTMP and if so, where? Nobody would want to see Red5 development being halted (and Wowza brings some healthy competition to the table) but would you expect Adobe to treat any major competitors in the same way? What if say for example Real's or Microsoft's server products became RTMP compatible, using Adobe's proprietary and potentially patented protocol? Or would that maybe be a good thing? I don't think we can simply point at AMF and say 'that's what they should do' because I believe that AMF and Remoting never made Adobe any real money, and at the end of the day that's what they aim for - generate revenue. And that's definitely not something I'll blame them for. The point being is this: it's much easier to 'give something up' such as AMF that is of little value in terms of the revenue it generates, but of great value to developers.
I'd love to see RTMP being more open, but I would not like it to be traded in for the future of FMS. Maybe Adobe should consider adding RTSP support to the Flash Player instead? I'm glad that I don't need to make these decisions.