One could argue that Word embeddings are also dimensionality-reduction techniques: Words live in an infinite dimensional space, and the embeddings is a finite-dimensional projection of this infinte dimensional space.

I think of word vectors in the opposite light. Words stored in a dictionary have 1-dimension (their index), making comparisons more or less random. Word vectors augment the information you have about a word by continually examining the context that the word appears in a corpus of text.

In fact, the typical way to visualize word2vec embeddings is t-SNE.