Why do video games award points in multiples of ten?

Because of the singular "1 point" vs. "10 points". All the messages are displayed using plural and the programmer can go home at 5.

Pure speculation, but I suspect it's (a) limitations of the early hardware (b) psychological.

With (a), it's less memory to store 1 than 10, but easy to display a zero as if you had 10. This becomes significant for larger scores I guess.

With (b). Do you want your high score at 100 points or 1,000 points?