You mostly had it yeah, MC is the monte carlo win rate at the end of the primary variation. Value Network is the neural network estimated win rate for that variation.
Playouts is the # of simulations ran down the branch that is bring printed. It isn't the total explored, but I didn't want to make the chat message even longer. You'll see when playing Leela using the GUI that she sometimes changes her preferred move over time. So a lot of work may have been done on a prior move that ended up not being played, making Playouts lower than move than in other moves.
If you see a number that is super low, it might be a 'snap' move where the policy network (a neural network predicting the most likely move a human pro would make) is so strong, Leela just makes that move herself without searching.
When you run Leela's GUI, open the Analysis window and start Analysis, and it'll constantly be updating while you play. The terminology I use on OGS is more similar to what gets printed out while running in bot mode, than what the columns are named in Analysis window in the GUI.