I just can't buy into that last sentence. I'd be kidding myself if I wanted to believe that Dream Theater influenced anyone outside of a handful of select bands, let alone change the course of an entire genre. Yeah they used to fuse technicality and metal in a very interesting direction but they hadn't really made an attempt at a truer metal song until "The Glass Prison" and aside from that song they haven't done anything of merit with that combo since. Very few of their metal riffs from that point have honestly wowed me to the point where I thought they were pushing new ground. If you want to talk about how they were instrumental in bringing technicality to the stage to elevate metal there are a lot of technical death metal bands my roommate has shown me that demonstrate more technical and theoretical approach to pure metal than Dream Theater has. Granted they're not my cup of tea and DT is much more tasteful in their approach but they are by no means close to the technical limit you're saying they pioneered compared to some other bands whose sole aim is to see how far they can push music theory.
Okay, I wasn't going to get into this discussion, since I like little metal from the last decade, but now I'm a little too interested.
Just because DT's metal wasn't that chunk and balls and there were bands who pushed technicality further doesn't mean DT's influence on metal in terms of technicality can't be that high. They were simply a band which a good audience latched onto in that respect. I used to read a lot of metal mags; I remember the article hyping Mastodon's Remission, and A7X's second album, the one before City of Evil. Both times, they asked the band five albums which, combined, influence their sound. Both bands said Images and Words. In fact, it was interesting how often they were mentioned by bands you'd never think would associate with them.
I mean, look at '90s metal. The early nineties was the "dumbing down" and commercialising of thrash, and groove metal, and the late nineties was nu-metal. That's only looking at the major trends, but just like in rock, the nineties weren't good times for much of any overly great display of technicality in metal. The focus on how well you could play your instrument rose very obviously in 00s metal, even in your everyday, not trying to be extremely technical bands. Compare Korn with A7X. Compare White Zombie with Trivium. A lot of thrash bands have gone from slowed-down metal and hard rock experiments back to their more signature thrash. The fact that DT were there at all during the nineties doing prog metal with a half decent audience... I just think they very likely had quite an influence on the swing back in that direction, even if it's more of a latent influence. Which means their influence goes far further than just your prog/power metal copycats, it's arguably across the entire genre.