Someone once told me that having all of that web dev knowledge can actually help in Machine learning, my question is how?

Beats me. I have a PhD in machine learning and I never once used anything even vaguely relevant to web development in my research. Literally any other thing you could be learning in computer science would be more helpful to ML than web dev skills.

To be honest, web dev - and I say this knowing I'll probably upset a lot of people - is easy to pick up the basics. When you're a well-rounded, experienced computer scientist, stuff up like CSS, JS, HTML etc. is something you can learn over a weekend.

Becoming a consummate expert at web dev, though, I definitely won't claim that is easy, because it's not and that would take a lot of practice.

If you want to do a PhD in machine learning then you should focus on things like formal methods, become skilled at at least one programming language (Java or Python are popular options), have some basic-to-intermediate level knowledge of statistics/linear algebra/discrete maths (or whichever is most relevant to your preferred area of ML study), have a strong understanding of data structures and algorithms... basically just know a lot about a lot of computer science topics. Web dev really won't help you much, though.

But, I absolutely agree with you it's a useful skill to know the basics of Web Dev, even if you don't intend to or currently need to use these skills.