Incidentally, that list is wrong; Isiah Thomas won his second and last championship in the 89-90 season, not in 91-92 or 92-93.
The titles went like so:
2007 SAS
2006 MIA (Jason Williams is pretty much pass-first but stupid)
2005 SAS
2004 DET (That different from Isiah? Not as good but similar)
2003 SAS
2002 LAL
2001 LAL
2000 LAL
1999 SAS
1998 CHI
1997 CHI
1996 CHI
1995 HOU
1994 HOU
1993 CHI
1992 CHI
1991 CHI
1990 DET (Isiah Thomas was the team's leading scorer)
1989 DET (Thomas = leading scorer after Dantley was traded)
1988 LAL (Magic)
1987 LAL (Magic)
1986 BOS (They had DJ, if you want to count him, he ran the O a lot)
1985 LAL (Magic)
1984 BOS (DJ?)
1983 PHI (Mo Cheeks)
1982 LAL (Magic)
1981 BOS (Does Tiny count?)
1980 LAL (Magic)
Of some note is that there have been several Finals squads with more conventional point guards.
Chicago and Los Angeles (the three-peat) won titles using the triangle system, one that emphasizes big guards and action through the wing players and the post as opposed to a small point guard. So that's 9 years right there. The Spurs have been using Parker and yeah, he's been a scoring guard but you also have to consider pace and the other weapons on the team; Parker's playing next to a gifted post passer and an excellent wing passer (several, actually), so he was never going to be a high-volume assists guy.
He's not necessarily a "pure" point guard but he doesn't shoot all that much, he constantly sets the offense up at the top of the circle, runs the pick-and-roll with Duncan a lot, etc. It's hard to call him something OTHER than a pure point guard. He's only taken 13-15 shots since his second year, he's not really a scoring guard, he just posts numbers because of efficiency and the fact that other teams can't really double-up on him too often because of the weapons elsewhere in the floor. He's kind of what I envision Monta Ellis being, eventually, at least stylistically (and Monta's a better mid-range shooter who finishes similarly well around the rim).
Bgil's comment is a good one; teams that don't look like they have as much structure are usually read-and-react offenses. Or something like Phoenix. Everything about their fast break is broken down by options, separated into primary and secondary break options, they get chances for quick pick-and-rolls, pull-up jumpers, etc.
Even the worst NBA coaches have at least something going on with their team.
Plus, structured offenses are almost a relative term as well, right? EVERY offense is read-and-react to some degree, even if they have opening sets which they prefer (and in that case, even the Princeton and Triangle and full Motion/UCLA offenses have a couple of key opening sets).
A natural point guard is a rare thing because he's usually a player with more scoring ability than he's using. Most guards (Iverson, Marbury) end up taking that a little too far and thus take themselves out of the territory of a primary playmaker whose focus is on distribution rather than scoring. With some guys, it's almost a tough call because of the volume of their production but you have to consider efficiency (Nash, Paul, Parker) and their basic role. Nash and Paul are pretty clearly pure point guards, it's what they do and they don't shoot THAT much (certainly not Nash) and even Parker doesn't shoot all that much, just about as much as Paul and he gets fewer touches because there are other playmakers at key positions in San Antonio's offense as I mentioned before.
Bgil, by the way, that's awesome.