At the time the DX7 came out, sample-based synths were still too expensive for the average musician. Affordable analog synths had less polyphony and mediocre piano sounds, plus they were heavy! The DX7 was cheap and light and did an alright piano sound, which is just what musicians wanted.
But having a cheap and light alternative to sample-based synthesis wasn't just useful to musicians. Cut-down versions of the chips also went into Sega consoles, Neo Geo arcade games, AdLib sound cards for PC, and even the early Sound Blasters.
I think Yamaha's FM synthesis had a huge impact on the sorts of music a whole generation of gamers grew up with, as well as being ubiquitous in pop music through much of the 80s. This is what makes the DX7 important, in my opinion. It's more significant as part of the story of consumer electronics becoming affordable than just as a pop music phenomenon.
[1]: https://www.youtube.com/watch?v=LCFqF-IeeAk
They were a combination of FM and early sample chips, but all super tasteful (as far as 90s game soundtracks go!) and exploiting the maximum of the chips.
The DX7 just happened to be positioned to capitalize best on this trend, as well as being useful live gear, but the quick move towards sampled instruments afterwards indicates how interchangable the sounds themselves were.
The DX7 mainly was an affordable all-rounder that got loaded with a ton of already-good presets and a way of managing presets. Yamaha had already released the GS-1 three years prior, but obviously it didn't remain in the books of history quite the same.
The Sega Genesis soundchip, YM2612 is also a great showcase on how different FM synthesis can sound compared to comparable competing consoles.
If anyone is interested, there's a great open source soft synth called Dexed, which is compatible with DX7 soundbanks (and comes bundled with a lot of em). A free, fun way of getting a glimpse into FM synthesis and music production techniques of yore.