I found the article a bit dull. And I'm a feminist. I do wonder what people hope they will achieve by preaching to the converted.
But that aside, I do think the current sexism in the world is hurting men as well as women and the issue with male loneliness is part of it. Whether it's true or not that it's worse than women, I think the argument to say it's the same is easily debunked by looking at male suicide statistics. The argument in the piece is they're only more different because men externalise their pain more. I'm not sure it really makes a case for that being unequivocally true. There's nothing evidential there.
Problem is to a man with a mental health problem this could read as minimising his pain.
Personally I do think there is something going wrong with some men and how their changing place in the world impacts mood, wellbeing etc. When you lose meaning, it can be disastrous for mental health etc. (Read Viktor Frankl's work). It's not a surprise to me that the manosphere idiots are gaining ground with this backdrop. But as in all things about sexism being the root of it, it's not down to one gender to fix it all.
Rather than hector people about what they're doing being wrong, I'd rather persuade by all of the stuff men are missing out on right now by not tacking sexism head on. This could be a joint effort. It could be about building communities which rival those that lonely men find online. Instead it places all the onus on men to make change at the end of a very very long diatribe. Much as I'd like that, that ain't going to happen.