If the entire play session is mostly or entirely improv in conversation with the players, as in story-now type games, then yes, I would think that is non linear. However of a "trad" style game that Colville appears to be advocating in these videos, improvised details come in the context of a linear, plotted adventure. So for example he says that a linear adventure can still be a sandbox, because the sandbox part applies to how players will solve the scenario, not in choosing which scenario they want to address. Basically the dm gives the players a mission, and there is a social contract at the table that the pcs will go and do the adventure that the dm has prepared, but how they approach the mission (combat, stealth, social) is up to them. So in that context, the PCs could try something unexpected, and the dm would have to improvise details. Maybe they try to sneak in through the kitchen and the DM has to come up with a cook on the spot. He seems to be implying that it is important not to let the players know that the cook, maybe even the entire kitchen, is made up on the spot, because it would spoil the illusion of a richly detailed location.What I was confused about though is how a DM who does as Matt Colville suggests and improvises things but endeavors to create the illusion that it was all planned out in advance, could be seen as running a linear game. Isn't it kind of nonlinear by definition if it's being improvised?
I get the appeal of this kind of dynamic between DM and player, and is probably what I'm most used to. But as a DM, I find the burden of maintaining this illusionism leads to burnout and is not fun, and as a player, I can see where a DM is trying to guide us towards their planned content, and it reduces the sense of player agency.