Where the objective function of Skip-Gram Negative Sampling (SGNS) come from? is effectively a more general version of your question. My answer there should answer your question.
In short, word2vec learns to classify which words (called context words) appear around a particular (target) word from those that don't. The dot product is just a simple model design choice, like choosing a simple linear regression model.
This prediction task is actually a slight red herring as the main aim is to learn useful word embeddings. It just turns out that training that model to be good at that classification task gives good word embeddings. That is not theoretically obvious, but followed from empirical observations that vectors taken from language models gave good embeddings with interesting semantic structure . Recent work aims to explain why word2vec embeddings have this structure [e.g. 2, 3].
 Linguistic Regularities in Continuous Space Word Representations (https://www.aclweb.org/anthology/N13-1090.pdf)
 Analogies Explained: Towards Understanding Word Embeddings (http://proceedings.mlr.press/v97/allen19a.html)
 What the Vec? Towards Probabilistically Grounded Embeddings