<Don’t the winds get their energy from solar radiation? It's not a closed system. An increase in wind velocity is not the result of a decrease in the earth’s angular momentum and vise versa

An increase in westerly wind velocity is what they're assuming here. The pressure gradients produced by solar heating would (I'm guessing here) on average not have a strongly preferential direction.

It probably would be influenced by the direction the Earth rotates and Coriolis effects and all sorts of other fluid effects which can't be easily expressed in english but the assumption is the time average of the effects would be zero.