I don’t understand this, is that not how most tables run? The rules cannot be engaged most of the time? Or are other groups rolling dice for every declared action?
Depends on the table and the rules.
They're all actors and voice actors. So RP is huge, obviously. But they also make rolls for persuasion and deception. So they engage the rules more than some tables in that regard. A lot of tables have no, use no, and want no rules re: social interactions. Matt's also adamant about perception checks. Making the players roll basically any time they want any information. Which some tables do, but some don't.
This surprises me as I feel it is the complete opposite. The CR players really interact with the environment from what I’ve seen and are constantly coming up with creative solutions. It would be pretty dull otherwise.
We're defining "interact with the environment" and "creative solutions" differently, then.
What I mean is a player describing something in detail that then bypasses having to roll to accomplish that task. The player is creative enough in their thinking and description that rolling for it is obviated. I've watched almost all of CR. I can't recall a single time that's happened. Matt invariably calls for a roll. Search for secrets doors. Roll. Search for traps. Roll. Look down a hallway. Roll. Give an amazing speech. Roll. He auto-succeeds on stuff like walking. But he defaults to rolling for basically everything there's a mechanic for.
The ur-examples are a 10ft pole tapping the floor for pit traps and descriptive searches. They haven't had that situation in the game that I recall. But I get the impression that Matt would still have the player roll for it rather than simply tell them, yep, there's a trap. Likewise with searches, Matt always asks for a roll. The players don't describe things in detail, they literally call out a skill and throw a die. Likely because most of them are newer to D&D and those who might have otherwise done the descriptive bit are so trained by now that simply rolling is easier all around.
There were a few times in campaign two where Liam seemed visibly upset that Matt refused to describe something unless Liam rolled perception first. Some that stick out are when they were walking toward the docks in some coastal city and Liam asked if there were any ships in the harbor. Matt called for a perception check. Despite them being on a street with a direct line of sight to the docks. Something similar in the same or a close episode where Matt described a tall tower at the center of the city that loomed over all the other buildings...and the streets were laid out like spokes on a wheel surrounding the tower, so line of sight the majority of the time...so at one point Liam wanted to spot the tower and orient himself based on that. Matt called for a perception check. You know, despite that tower being 100-or-so feet taller than every other building in the area and the majority of streets leading directly to the tower in question. And again later in Aeor. Liam was at an intersection and asked what was down the side hallway...Matt called for a perception check.
That's literally the opposite of what I'm talking about.