Air France were also round-the-world once they took over UTA in 1990. UTA had operated from Paris across Asia to Noumea and Tahiti, and thence to LAX. Air France operated from Paris directly to LAX, so after the takeover they were RTW. This link has now been broken.
The UTA flghts from Paris through Tahiti had some strange features. The sector that had the highest frequency was from Tahiti to LAX, but the operation was based in Paris; aircraft had to be operated the "long way round" out from Paris to Tahiti, then to operate to LAX and back maybe multiple times, and finally back to Paris.
There are several all-cargo RTW operators as well, for whom I believe TMA from Beirut were the pioneer with cargo 707s around 1980. Federal Express have round the world MD-11s nowadays.
The Pan Am "round the world" operation was always characterised by not only a gap across the USA, but also aircraft changes of type/gauge along the way as well, even back in prop aircraft days - and the 747SP was a initial request from them to have something smaller than the standard 747 for the sectors between London and Tokyo.