Sure power played a role, but imho, it was a lesser role that was always overblown by fans and the media. There's plenty of guys who were/are in his ball park power-wise, but far fewer who had his short game skills and mental strength (he's in a class by himself on the latter, at least among his peers in the last 15 years).
When Tiger played his best golf under Butch only Daly was as long, and the distance advantage was a huge part of Tiger's psychological edge over everyone else. Guys started to catch up when technology changed and Tiger stuck with a steel shafted, 42 inch driver until he was forced to switch to graphite to keep up. It's hard to tell where Tiger stacks up in terms of distance now because he's played so poorly recently. Guys lile Bubba and Dustin Johnson are clearly longer and Michelson is probably as long (which would have been unthinkable in 2000). Dominent golfers of any era are almost always long hitters. Hogan may have been an exception in his best years (although he was a long hitter before the accident) but his ball-striking was unique.