Your computer can definitely run 20 game jam games. Game jam games don’t usually have the best graphical quality.

Incidentally, if you are referring to the following excerpt, the rules mean that your own game has to receive 20 votes, not that you need to cast 20 votes. Although it is indeed good practice to vote on many games to help others. :)

Your game needs to have at least 20 ratings to be eligible to win, so make sure to play a lot of games, so your own game has a higher chance of being shown to others!

It is alluding to the Karma system, which puts forward (in the ‘Most Karma’ ordering) those that rate and comment other games, relatively to how many votes they received themselves. So, if you have few votes but rate and comment many games, your game will probably show up amongst the first ones in Karma. This was designed to encourage people to review others’ games and get a fair share of the votes.

Which is why, by the way, people should use the Karma ordering when searching for games to rate (and review them)! (I personally use both the special list of games with few votes — a hyperlink shows up at the top of the entries page — and the Karma ordering.)