They could:

• hack the game code statically (find the routine that sends the score and change the assembler to modify the score just before it's sent.
• hack the game code statically and multiply all the points that are assigned by (say) 2 so that their score is higher in-game.
• find the code that does the encryption, extract it and write a little command-line tool to submit whatever high-score they choose.
• break the encryption (probably by disassembling the code to figure out the encryption scheme), then intercept the TCP packet before it leaves their machine and change the number.
• ...
  

Sorry I never realised that anyone would go to such an effort just to get a high score for something as unimportant as a game.

I wonder just how many such sad people there are out there?

Well, the first and second options aren't really that difficult (particularly if function symbols are still in the executable). I mean, there's at least one game I've used GDB to get around trial period expiry so there's undoubtedly other less scrupulous people who'd think hacking their way to a high-score was good fun...