The chess game that Locke beat the computer with was a famous game from 1985 between Kasparov and Karpov. Perhaps the machine was pre-programmed for this game so that replaying these moves would be a way to activate the manual override.
The Others had to leave someone stationed at the flame to initiate Food Drop Protocols either for supplies or to maintain the illusion that the Dharma Initiative was still functioning normally on the Island.
Whomever Michael was talking to from the Swan computer was using the Flame computer to initiate contact.
The chess game is really a password system, and that exact game set must be played to access the command interface.
* Locke's opponent was actually a person. Locke says as much when he notes, in response to Mikhail's comment, that only humans can cheat. We see a shot of a camera, so we know that the scene could be observed. (The camera that is shown appears to be too high to be the camera that Mikhail cut off when he was observed from the Pearl.) The observer wanted Locke to reach the Candle video and so allowed himself/herself to be checkmated. This would explain how Locke could beat the game so readily.
This could be the same person who activated the intercom at the Hydra for Jack.
Cheating at chess is near impossible, beyond asking someone else for help. Cheating was probably just a reference to the machine being "too good"
By saying that the computer 'cheats', Mikhail was really saying that he was unable to gain manual override by beating the game. Mikhail spent his time in the Flame trying to beat the chess 'password protection', expecting that winning a game would get him access to the subsystem. It didn't, so in his estimation, he was being cheated. Locke figured out, either by accident or by foreknowledge, that 'winning' really meant entering a very specific set of moves.
In video games, a special set of keystrokes or button combinations used to unlock hidden features can be referred to as a 'cheat'.
Having to take at least several minutes to enter the chess moves is a cumbersome way to initiate an "emergency" self-destruct mechanism.
The chess game could have been one of the increased security measures for the Island network mentioned on the blast door map.
Compared to the programming on The Swan and The Pearl Computers the chess game seems to be a recent addition, more options could have been available before but were hidden, and the true function of "77" was disabled and linked to the C4 bombs.
The background in the back of the Flame video is distinctly reminiscent of the background of the room where Sayid finds the DHARMA binders. Is it possible that Mikhail didn't know that Candle was right below him giving the message options on the computer, and then found out when the purge happened...or Ben knew Mikhail would get mad if he knew someone was right under him, and possibly spying on him. (Mindgames)
Entering 77 does not actually destroy the Flame, but it gives more important information, and then it told John to enter another code to detonate the building; Locke just acted as if he didn't know what was about to happen. He did, after all, lie about knowing there was C-4 in the Flame.