I don't remember much segmentation.
The people who played Quake moved to Quake 2 and Quake 3 and Half-Life, for the most part. It's just that of the three Quakes, Quake has the most long-lived single-player experience.
Half-Life was competing against Quake 2, which was a year old by the time Half-Life came out. I think the general consensus is that Half-Life is just a much better game than Quake 2. Quake 2 had a much better competitive multiplayer experience than Half-Life (my opinion), but Half-Life was much more fun for casual play. The players that moved from Quake to Quake 2 moved to Half-Life.
Steam wasn't a major factor early in Half-Life's release cycle. Half-Life was released in 1998, and Steam didn't come out until 2003. Before then, you'd update Quake, Quake 2, and Half-Life the same way... you'd see a news article on Planet Quake or Planet Half-Life about a new patch and download it, or you'd connect to a server and you'd get an error message. Quake did get updates for a fairly long time, considering... QuakeWorld 2.33 came out in December 1998, when Half-Life was already out. Quake 2 got updates for a while as well, but the online experience of Quake 3 was far superior, and Quake 2's single-player campaign just wasn't great, so not many people cared about Quake 2 updates late in the game's lifecycle.
> Back in the day Quake series was the big games, not Counterstrike. ID Softwares lack of investment opened up the door for Valve.
> It was theirs to loose and they lost it.
Half-Life was just a better game, overall, than Quake 2. It wasn't a lack of investment.
There are various theories revolving around the major "personalities" at ID Software, but I think it's enough to just say that Quake 2 was not as good as Half-Life.