The problem is nice but the solution proposed at the website is too convoluted. The straight solution is simple. The mid door must say the truth, so left and right doors must lie. Taking these three simple facts into account, the exit is on the right door.
The solution only works if you modify the rules. The rule needs to say they always lie about which door to take. If they "always lie", then they would be forced to always make a false statement, including lying about the rules.
My brother, who is a knight, says this is not a Knight's and knaves problem.