Nobody mentionned SyntaxNet or LinkGrammar. If you did not read the article from Chomsky about the two ways of doing AI you should read it. Basically it says there is statistical methods and logic methods in AI. Most of NLP libraries of today use the statistic approach. The other, the logic rules based approach was the most popular before now. Anyway, that's what does Link Grammar. I recommend you start with the introduction https://amirouche.github.io/link-grammar-website//documentat... to get a feeling of what it means to deliver meanings to sentences.

Also nowdays, word2vec is unrelated to the understanding of grammatical constructs in natural languages. It's simply said a coincidence or co-occurance of words. Grammartical interpretation of a sentence must be seens as a general graph whereas word2vec operate on the linear structure of sentences (one word after the other). If word2vec had to work on grammatical constructs it should be able to ingest graph data. word2vec works on matrices where the graphical representation of the grammar of sentence (POS tagging, dependencies, anaphora, probably others) is graph otherwise said a sparse matrix or a matrix with a big number of dimensions. (It seems to me machine learning is always about dimension reduction with some noise).

I am quite ignorant about the literature on the subject of machine learning operated to/from graphical datastructures.