So, it is based on the article below: Go to the bottom of the article where the 'Mario-Kart Speed Boost' example is.

So, the intuition in the examples makes sense to me but sometimes people explain things clearly but incorrectly. Maybe this is one such case.

https://betterexplained.com/articles/vector-calculus-understanding-the-dot-product/

Some Q's: a. Is the dot product in this case telling us simply about the amount of boost that will be assigned? b. is it telling us anything about speed?