There's actually a few reasons people think, erroneously, than Critical Role and other live-play games are scripted.
1) Instant Response. As noted, everyone involved is a professional actor with at least some background in Improv. They're all thinking quickly on their feet and they've all taken a lot of effort to inhabit their characters. Things like Keyleth jumping off the cliff to try and hit the water, below, was not a scripted event. It was an off the cuff in character decision that turned out REALLY BADLY. Turning into a goldfish REALLY didn't help the situation, but it's what jumped into Marisha's head in the moment and she acted on it.
2) Prop-Work. Not just the prep-work of the DM to cover all kinds of contingencies, but the art department having various props and sets and stuff ready in advance. I would hazard a guess that while most DMs know the "Coffee Stained Paper" prop-making method, most DMs have also never used it. That the majority of us go "Oh, that's so cool! I wish a DM would do that in a game I'm in..." and move on with our lives. But not only are there DMs out there who spend tons of time making props like that, Dimension 20 has an Art Team to do it professionally, as an example.
3) Incredible Teamwork. The groups almost always seem to work together incredibly well and find/follow the plot pretty directly. There's a few reasons behind this that a lot of players don't get, but make a ton of sense. Firstly, Matt Mercer knows and has played with these people for over a decade. If he drops a hint, they pick up on it because he's learned with a ton of experience precisely how braindead obvious he's got to make something for the group to pick up on, and they've learned that when he drops those hints they should chase them. Secondly, They're friends playing a game together who talk about the game outside of the game itself. There probably are -some- little side-bits that a given player has essentially 'scripted' just like people plan arguments in their head in the hours before a confrontation. And, finally but most importantly: they've long since gotten rid of some disruptive elements.
Anyone remember Tiberius Stormwind as portrayed by Orion Acaba? He was often at odds with the other players in the first 27 episodes. He'd extend the shopping scenes well beyond what anyone else wanted and slow the game down, get into arguments that derailed rather than enhanced scenes, and sometimes stop the game, entirely, to try and convince Matt Mercer of how the rules "Actually Worked" in his favor. He left for "Health Reasons" but there were accusations of metagaming and cheating floating around the community months before that decision. Like to the point where the player sitting next to him at the table would be checking his rolls because of how he'd get on indefinite 'hot streaks'.
How many other players have these players dealt with who were similarly a poor fit for the group before they left and the remaining group that fit well together slotted into place? We don't know 'cause before Campaign 1, none of us were hanging out with them. (I assume)
4) It's Expected. This is probably the biggest one. When you see something done professionally with a bunch of people on a set with cameras rolling you've been raised to expect Cue Cards or Teleprompters. Whether that's Saturday Night Live or a Political Rally. We even know that the majority of Reality TV has scripted elements and deceptive editing to result in cohesive plotlines and dramatic scenes being paced out.
5) Time Investment. Pretty much every session is between 3-4 hours and they always seem to get SO MUCH DONE compared to a given table's home-game because they know each other and the rules pretty well and just go and do the thing. They always seem prepared to deal with problems as they arise and there's rarely times where people completely misconstrue the setup and make-up of a scene, resulting in a sense that every scene has an allotted amount of time so they can get to the almost inevitable cliffhanger at the end of the session without going over... but they OFTEN go over, or end early.
The first nine episodes of Season One are just over 3 hours for most of them, but there's a 2:36, a 2:57, a 3:58, and a whopping 4:42. Why? To get to the stopping point. Or to stop -before- a section they know is gonna take 2 hours to resolve when they've got a half hour left.
I wouldn't say its tightly scripted with a telepromter and such. However they make a very cushy living doing crit roll. They know their job is to be entertaining, not to actually play a game. So everyone acts and plays in a manner that plays to the audience.
Remember, they make millions per year doing this. Its not "for funsies", its a business, so they will treat it accordingly.
Do what you love and you never work a day in your life.
They do it for fun, -and- for profit. Also bear in mind that Critical Role is -far- from the only thing these folks do. They're all still Voice Actors and appear on Youtube Channels for things like Smosh or React. They play in other people's games, rotate in other DMs, etc. Hell, Ashley Johnson has to do a -bunch- of episodes remotely across the series because she's acting in shows or movies or plays elsewhere in the world and can't physically make it to the sessions but doesn't want to miss a week if she doesn't have to.
It's not scripted. It just -looks- effortless.