It's a combination of two ideas: to psych someone out, and to outdo someone at something.
To psych someone out is to put the idea in their mind that they will lose, to successfully bluff or intimidate them, to play mind games with them so that they will do what you want them to do. If a team psychs out another team, they scare them, they give the impression that they're unbeatable. If a parent says, 'Oh, I'm sure you won't like asparagus, it's really for grownups,' the kid might say, 'You're just trying to psych me out to make me eat more vegetables.'
The prefix out- can be used with many verbs. It means to do something better than someone else (at a specific time or on a particular occasion), to excel at that activity. If you outsing someone, you sing better than they do, you win the singing contest. If a team outplays another team, they play much better (and usually win the game).
So in your sentence, the speaker is saying, Maybe they just convinced us that they were better than we are, and that's why they beat us, but they might not really be as good as we think.
(Notice also that the first part of the sentence has a mistake. It should be either 'They've beaten us in the district playoffs before' or 'They beat us in the district playoffs last year.')
If the German speakers can come up with some translation suggestions, 'to psych so. out' would be a good New Entry.