Common GloVe equation has an error?

[Nicholas Gunther]

One common GloVe equation (see, for example, slide 24 of the public slides for the second lecture in Stanford CS224N NLP with Deep Learning | Winter 2021 | Lecture 2 - Neural Classifiers )  is:

w_i \dot w_j = log P(i | j)

Image:

BUT in general this is wrong.  As a dot product, the left-hand side is commutative in i, j while as a conditional probability, the right hand side is not. 

Can someone indicate the correct statement?  Or please tell me what I'm missing?

Thanks!

- Nick