Uh yes of course there were several competing potential suppliers of light sources (just as there were entire EUV systems) but all the other ones didn’t work and were not close to working. That is the definition of a critical enabling technology. Cymer was in fact the only game in town.
Only one that worked is patently incorrect, since early ASML R&D units shipped with non-cymer EUV light sources (some Philips collaboration iirc).
Best performance at the time maybe (be it reliability/output power/size/..), but not the only one that worked at all, so no..
I don't think that was true. Gigaphoton achieved similar numbers to Cymer roughly a year later with a very similar design idea (so unclear why they would have had no path forward? they are still on-par today with Cymer as far as I can tell), XTREME was not too far behind (within factor 3 I would say).