[WARNING: This post contains spoilers]
The space odyssey breaks down like this: a curious black obelisk pitches up on pre-historic earth and does something - it's not entirely clear what - that causes monkeys to evolve into homo sapiens. Wind the clock forward four million years and another obelisk is discovered on the moon. Whoever left it buried there did so in such a way that ensured it would eventually be found and when the strange object fires a signal in the general direction of Jupiter humanity decides it might be a good idea to head out there to sort out what's going on. It is on this long old journey that we find Frank playing chess against a HAL 9000 computer.
Hal's "I'm sorry Dave, I think you missed it" foreshadows the considerably more sinister "I'm sorry Dave, I'm afraid I can't do that" which will come half an hour later. Other than that, though, at face value there doesn't seem much to this scene*.
It all just a little hackneyed, no? Well yes it is, but only because it's been copied so many times since. In 2001 we have chess as something you do when you have a huge amount of time to kill and not much to do (The Thing) and we also have a 'computer besting humanity at the game' storyline as a shorthand for technology advancing far beyond humanity's ability to cope with it (Saturn 3; Blade Runner).
The 2001 chess is rather commonplace to us now, then, but it must have been rather special at the time. Think about it for a moment. The film was released in 1968: humanity wouldn't arrive on the moon (or not) for another a year and colour television wouldn't be standard in British homes for a decade**.
Forget that the computer won. Considering that the bat and ball tennis game that made an occasional 'blip' sound would be state of the art for video games throughout the 1970s, just playing a game of chess against a machine must have screamed "INCREDIBLE FUTURE AHEAD" to the folk who saw 2001 when it was first released.
Chess Goes to the Movies Index
* There is a school of thought that suggests that the chess game is actually a hyper-subtle early clue that HAL is going to malfunction. This is based on the fact that (a) he says "queen to bishop three" when he means "queen to f three" or, more likely, "queen to bishop six", and (b) he apparently overlooks that White can delay mate for a couple of moves by not taking the queen. With all due respect to Mr Stanley Kubrick, though, I'm rather minded to believe these discrepancies are much more likely to be mistakes.
** The first FA Cup final I watched in colour was Ipswich 1 Arsenal 0 in 1978.