My avatar is from the chilren's game Monster Mash
What I mean by that is that not only knowledge or pure reasoning should prevail, but some personality traits as well.
Your games are very fine, but I should state, that the occasion is more a party or an event than a boardgame-evening.
Ah yes... Those recommendations were pretty bad then...
It seems a hard recommendation to make as it seems like you're looking for games that could reward creativity or some other stuff which would seem to be easier to find in party games... But those are rare for two players only...
I'll still make two other recommendations but they are probably a bit far fetched...
Bunny Bunny Moose Moose: A third player needs to be the referee... Personality traits required: good reaction to stress and quick counting (if that counts as a personality trait).
Concept: Needs to be adapted. One possible rule: make the audience guess as many clues as possible in a set time. You do need to involve the audience but I feel that could work...