If there was any change, it came more from Final Fantasy 8 imo...
Especially the CGI, the change is much more evident in VIII than VII imo if you look at how often it's used but in particular what sort of scenes they're used for... I was just thinking about that the other day, actually. Having replayed VII recently, it's really not all that cinematic per se. It's story heavy, to be sure. A lot more dialogue than VI. But the conversations are often still primarily presented in a way very similar to VI. And the primary storytelling method is still dialogue. CGI was still rather conservative, and it was really as a reward, used specifically for action set pieces. To this day, I feel VI and VII are very parallel to one another, and VII is very much like a natural evolution of what was done with VI, not only thematically 'world in danger' and 'steam punk/diesel punk', the esper/materia systems, but even the way the games use dialogue, uses pacing to break the game up into explore/reward for each segment of the game (namely from the overworlds being similar IMO), heck even how both games use a lot of comedy and goofy scenes. I feel like FF VI would have been told and looked a lot like VII had VI been a PSX game.
It was really with VIII where the CGI began to become so heavily used even more mundane things... even overused. Things like the introduction CGI for Quistis that just shows her walking through a door and smiling -- there's very little point to it. I remember at times playing VIII and feeling like, 'did we really just need to wait and load for a CGI to show thaaat?' But it's also where Sakaguchi really started to try treat FF like a Hollywood epic IMO, and you see that not only in the far greater use of CGI but also the greater focus on romance and the lack of comedy.
VII still reminds me a lot of VI in terms of overall presentation and story scenes, just a natural evolution of it. It's really with VIII that I felt it had a significant change it how it presents itself.
That said, I think any effect on JRPGs could be overstated. For one, there really aren't that many. So, if VII and VIII had any effect, it was sort of the COD effect that raised the bar so high that killed off too many smaller projects. I think you saw that somewhat in series like Suikoden III trying to present itself differently. But we still got Suikoden V. Still got games like FF XII. But a lot of that isn't because of VII per se but could just be the nature of the business.
I mean, almost every genre gets fewer classic games. Think of all the shmups, fighters (MK or SF clones), adventure or beat 'em ups (Batman/Double Dragon/TMNT/etc clones). I mean, fighters are different. Racers are different. Quite a few genres were different back on the SNES when teams could more easily make small games, and a lot of genres 'changed' at some point during the PS1-PS2 period. You could attribute every genre, not just JRPGs, to games like FF VII but also VIII, Shenmue, Tekken, COD -- everything become bigger budget (Shenmue), more cinematics or 'set pieces' (COD) or CGIs as rewards (e.g. Tekken), etc.