Having not done that tutorial and you not providing a capx, it is hard to guess at best approach.
Create Variable Level1, level2, level3 etc
On start of layout level1 set Level1 to 1. On start of layout level2 set level2 to 1 etc
Now you have a check on your map you can disable buttons or make sprites no clickable by putting in condition that level1 = 0
I see it uses some variables locationnumber and latestknownlocation and checks that player is greater than or equal
Just create a new event checking that player locationnumber is less than players location make invisible or whatever