Haiku predates Haiku Learning by several years. But fortunately trademarks don't generally work that way and lots of companies and products have, for example, the word "Windows" in their name.
From what I've seen, trademarks only limit name choices for direct competitors. That's why the existence of Apple (the music label started by the Beatles) didn't stop the name being used again by Jobs and Wozniak.
Looking at the sister Wikipedia link it appears that it did stop them from expanding their business several times in an audio/musical direction, until they coughed up some cash.
Apple Computers still settled out of court several times before then though. As early as '78 Apple Corp (the music label) sued Apple Computers with the computer company settling in the early 80s. So the disputes have been going on longer than Apples expansion into the iTunes et al.
Sure, but if you look at the trademark claims that were made, they were all based on some kind of sound/music-related activity (aside from the first set of claims, I don't know enough detail about the claims that started the case in 1978 and haven't been able to find much in the way of substantial detail online). Even if some of the claims were a bit of a stretch, it appears that the trademark claims relied on establishing that the companies had overlapping interests. It's probably harder for companies that produce general purpose hardware/software to defend themselves against these claims (compared to companies/products with a narrower focus), as there are more angles for lawyers to use to try to link them with other companies.
On a completely anecdotal level, I have some friends who were contacted by a big technology company as their coffee shop had the same name as one of their products. Once it was clear they weren't competitors, I don't believe this technology company contacted them again. This was further evidence to me that trademarks are not universal in scope.
Do these people have a registered trademark for haiku prior to 2004 in the same territory and classification? If so, yes. If not, no. (There are grey areas, but this is all it should come down to in theory).
https://www.haikulearning.com/
EDIT: I jumped the gun on this one. Should have done a bit googling first.