This is beside the point somewhat, but he never lost to her in classical chess. But what he did was worse than lose. He once played a losing move against her but realized it was losing...and changed the move to one that didn't lose. i.e. cheated. He did a similar thing with Nakamura a few years ago, which was ridiculous to watch. His opponents didn't protest, for whatever reasons. I don't know if it registers in his mind that he cheats. Sadly, that's the character of the greatest chess player of all time. Hopefully Magnus keeps playing a while longer and takes that title.
A great way to weaken a position is to make weak arguments in support of it. Externally, such a move opens an otherwise strong position up to new criticism. Internally, it invites internal dissension between those who agree on the main point.
On the other hand, I think people listen to his views on politics largely because he's well-known as a chess player. In a sense, people do the opposite of an ad hominem attack, by putting more stock in his arguments because of how respected he is in chess. We have to remember that he's as fallible as anyone else.
