No it didn't, psytrance came from goa trance for which the foundations were laid in the 80's before trance popper was a thing. And what is liquid trance? Never heard of it.
But not to make this post just about whining, here's possibly the first trance track ever made, since we're talking about it. https://www.youtube.com/watch?v=MT9pH9C7Oew I'm not from the 90's so I can only imagine how shocking this music must have been 23 years ago.
Psytrance came out of early german trance from labels such as Sven Vaeth's Eye-Q.
Eye-Q 1991: https://www.youtube.com/watch?v=lApfaxi0QZw
Harthouse 1992: https://www.youtube.com/watch?v=d146LKl2ixU
This was Goa in 1991: https://www.youtube.com/watch?v=3fnBz6IOolk a very special period in time
https://www.youtube.com/watch?v=VT7lwdui4HY
The KLF became more theatrical and were the biggest singles selling act in the world in 1991, then retired in 92, ceremonially burnt a million pounds and deleted their entire back catalog.
This sort of techno-poetry track from Anne Clark in 1984, "Our Darkness" seems related to "What time is love". Although its surely not trance.
I'm a kid of the late '80s and '90s and that wouldn't have been shocking for mainstream listeners back then. I'm especially thinking of Eurodance music which was pretty massive and popular in the early part of the '90s and which sounds very similar in some respects to the music in your YT link.
It's also true that times were different back then, and for the better, just look at the MTV Top 10 of 1994 [1] and you can see bands like GreenDay, Sound Garden, Nirvana or Smashing Pumpkins. These type of bands wouldn't make the top 10 of popularity charts in this day and age (with the exception of GreenDay, probably). I mean, just look at this "Black Hole Sun" video [2] from Sound Garden which 13-year old me was watching during prime-time on MTV while doing my homework, this was seen as totally normal back then. Nowadays I'm afraid these type of music-videos and art-creation in general are out of prime-time media. The '90s were a lot more daring than today.
But sadly and much to my dismay the 303 didn't last long in the scene. It's really hard to find any acid lines in goa/psy tracks after about 1998 or so..
Ellez Ria - Overdrive (Original Mix) https://www.youtube.com/watch?v=N8MoltyYRaM Acid lines are used pretty heavily throughout the track
Liquid Soul & Vini Vici - Universe Inside Me https://youtu.be/yvBK1rSUzTc?t=226 A acid line slowly filters in at 3:44
Liquid Soul & Zyrus 7 aka Talla 2XLC - The Future (Liquid Soul Mix) https://youtu.be/9Wm4PJszzuo?t=313 Two Acid lines start to filter in at 5:13
Acid eventually resulted in liquid trance, which eventually became psytrance. Liquid was a fantastic exploration of the nature of sound, with many types of dynamics for a single instrument. EDM receives as lot of criticism for its lack of humanity and skill (regarding playing an instrument), but the same could be said of Beethoven or Bach: they were merely creating scores for an orchestra to play. EDM can be the same type of approach, only we now have ways to explore sound that simply weren't available to the great composers.