There are three issues here: regulation, time control and technology.
The FIDE Laws of Chess cover over the board play. They do not cover correspondence, simultaneous displays, handicaps, variants (other than chess960), computer chess and anything else which is not strictly OTB, although you are free to use a suitable subset for these other forms.
Even if you are playing OTB there is no obligation unless you are playing in a formal competition which is governed by FIDE or an association of FIDE like your national chess federation. When I taught my kids to play, the touch-move rule came very late in my priorities.
The first time I played in a formal blitz tournament I had been playing competitions with standard rates of play for about 30 years. I was very familiar with touch-move. However the informal rule I was used to for blitz was that touch-move did not apply. Your move didn't become "fixed" until you pressed the clock even if you moved a piece, let go of it, moved it back and moved another one.
It is interesting that in the recent St Louis event in the Nakamura - Kasparov game where Kasparov violated touch-move quite blatantly, the commentators were unsure, Kasparov claims he was unsure and says (which you can actually see on the video) that he looked around at the arbiter for guidance to see if what he was doing was wrong.
In OTB chess played at standard time controls (each player having at least an hour for all their moves, more for stronger players) touch-move makes a lot of sense. Calculate your move in your head without touching or moving pieces around on the board and then make it.
In chess played online via a computer interface the vast majority of games are played at blitz rates (each player having 10 minutes or less for all their moves). Time controls go all the way down to bullet - just one minute for all the moves. That it is even possible to play a sensible game at these rates is down to the technology: there is no clock to press (the technology handles that), you can make moves (with practice and the right mouse) much quicker and you can pre-move.
The last one of these is key. There is a lot of skill (and even character) in pre-moving and in a format where speed is vital pre-moving can make a big difference.
FIDE laws regarding which hand you press the clock with, touch-move, how you capture a piece or castle (use one hand only, please!), how you promote a pawn just don't make sense in correspondence chess or in online chess.