That's not improv. It's ad hoc and random generation. Not quite procedural. Improv is where you are following along with the other players and adding to them.
Both yes and no. It is going with the results that brings improvisation to the front. Will they fight, will they parley? How it will go down from one encounter to the next isn't that far from pure improvisations. There are degrees in improvisation. In fact we have a game in Québec (well, it is practice in almost all French countries now) that is called: "Improvisation". I know, very imaginative... The point is that there are two teams. Each other are given a theme and they must build a story about that theme.
Improvisations can be mixt or compared. An improvisation might be solo, unlimited, limited, a balance of opposing players or it might be unbalanced. At the end of the improvisation, a vote is called for from the audience to see which team will get the point.
The game itself is loosely base on hockey rules where there are two teams, three referee, is played iver three period of 20 minutesnd. There are penalties for not playing with the improvisation that your opponent has initiated, a heavy penalty is also given for just trying to make people laugh and not playing into the improvisation itself.
Categories range from singing, poetry, silent, normal and in the style of an author or movie. Special points are given at the end of the third period for best player, best line and best sportsmanship. There is even different time for an improvisation ranging from 30 seconds upto 10 minutes.
The referee calls the improvisation in the middle of the stage. It might go like this. Mixte improvisation with the title: "Love at first sight". Time 2 minutes. Maximum of one player per team. Both twam now have 20 seconds to debate who should go and maybe a direction to take the improvisation. A team is made of four players and one captain.
I can even translate the game rules if needed, as I used to be a referee at this game.
So all this to say that improvisation is possible at various degrees. One form is no less interesting than the other and has as much merits as any other.