The bit at around four minutes is quite tragic. People rightly mocked Peterson for crying way too much...but at least he cared.

I'm not sure this is true, at least not for the clip featured. This was already late stage Peterson in Sept 2022, after whatever damage one may speculate he suffered from the benzos episode. Musk completed the Twitter takeover only one month later. By December 2022 Peterson was already ranting about 'anonymous coward troll demons'.

Whatever is making him cry here (and it wasn't the last time he spun some Tears For Piers) I think it's too simple to ring it up as pure empathy. Probably a lot of ambivalence and confusion which was making it difficult to know what to say or think. The deadpan 'sure. why not,' in response to Piers asking him whether he championed incels, felt like an unenthusiastic way to commit to that stance, so I think his stance was already changing.