You are correct that synth music as a genre existed before the DX7, and that synths were used in popular songs even going back into the 70s. But what this article is discussing, and what most people discuss when they talk about the DX7, is how its sales dwarfed that of any synth that came before it. It didn't just become a piece of equipment used by major studios in countless hits across many different genres, it also became an affordable and useful instrument for working musicians across the board.
Right up the top of this thread the first commenter explained it well: "The keyboard player's job moved from playing the piano or organ to coming up with all the accompaniment parts that aren't guitars."
What I don't know is if the DX7 itself was particularly recognized as a DX7 by most of the people listening to music that was made with it. My guess is that most casual listeners still just considered it "the thing that the keyboard player is playing". This is why I am not sure that it is as uniquely distinctive as the commenter near the top of this thread suggested.
Of course trained musicians can identify a DX7 in a track, just as they might be able to hear the difference between a Stratocaster and a Telecaster. Dedicated fans might also hear the difference, if they're interested enough to pay attention. But someone just listening to a tune on the radio, humming along to it, I don't think they're going to go "yep, that's the good ol' DX7 electric piano patch" or "yep that's a classic Strat sound".
Personally, I think laypeople do identify the 808 in this way, just judging from anecdotal conversations with people who are not musicians, not DJs, not "serious" music fans, just regular people. This is why I think the 808 is an interesting instrument, and perhaps special in a way that the DX7 wasn't, and the TB-303 and TR-909 weren't. That doesn't mean those other synths aren't special for their own reasons, I was just commenting on something I perceive to be unique about the 808 - a relatively widespread understanding of what its "sound" is.
If you are a hardcore music fan or a musician, it can be illuminating to do some testing with someone who isn't. Play them a song, point out some piece of equipment, explain to them why this song has a 909 hihat but that song has a 707 hihat, and how you can tell the difference. Then play them another song and see if they can identify the hihat. 9 times out of 10 that's not what people are listening for. That's not how they experience music, they don't break it down like that.