I am running a tabletop RPG, and want to create a small, text adventure connected to our game. The adventure begins in a room with eight open gates, and behind each gate is a particular puzzle. When a puzzle has been solved, the player is given a geocache coordinate and in the geocache is a physical prop that serves as a token to be used in the tabletop RPG (giving the PCs special powers). What I am aiming for is that when one of the puzzles has been solved, and the coordinates have been revealed, the gate for that puzzle is closed, forever, and cannot be opened. In this way, a player logging on to the game after 6 puzzles have already been solved (and 6 tokens found), finds that 6 of the 8 gates are now closed.
Is this doable?
You say "a player logging on to the game after 6 puzzles have already been solved", which implies that people can log onto the game and they all are sharing the same state. If you want to do that, you'll have to give them all the same login info for textadventures.co.uk so that they can share a saved game, make them load a saved game and then force a save when something changes. It's doable, but ripe for mischief (e.g. someone could bypass the saved game, run the original game, and solve the puzzles anew).
Another thought is that you could "encrypt" the game by using a password. That is, you must enter a password that you have been given after a particular puzzle has been solved. When that password is entered, it locks all doors where puzzles have been solved. Not much different than Jay's solution - players could still enter the first password given and start anew.
You could also create 8 separate games. The first has 0/8 gates locked. The 2nd, 1 of 8, and so on. It would be very easy to do that, too. Easier than creating a password.
Just two alternate options. All are quite doable.