As a linguist, I have no idea what this is supposed to mean. There have always been alternative approaches. But we have not recently been blessed with any that are clear winners in terms of simplicity and elegance.
Now, of course one can argue - as Chomsky himself has done - that statistical approaches are not as elegant as rule-based ones but as human language faculty quite likely behaves statistically to some degree, statistical methods for describing language do have some merit.
The term "statistical approaches" could mean almost anything. There have always been people who are more interested in building, say, practical machine translation systems than in figuring out how kids acquire grammatical knowledge. But again, the field has not "moved on". There are just different groups of researchers working on different problems.
I don't know a single generative linguist who is committed to the claim that grammaticality is binary. And there is lots of published work in generative linguistics that explicitly does not assume this. Where are you getting this idea from, exactly?
>language is essentially algebraic,
Not sure what this means. If it just means that sentences have structure, then yes, generative linguistics is committed to this obviously true claim.
>He repeatedly dismisses whole subdisciplines as "uninteresting," but in context those complaints don't mean "uninteresting to me," they mean "worthless."
He's entitled to his opinion, no? It's not as if no-one ever criticizes his work.