"Race" is a social construct, so people are whatever they are labelled. For the purpose of how they are treated in Western society though, no, Muslims, particularly Arab Muslims are not white.
So that person pictured in the OP is not white?
Beet's first point in that post is actually correct. Race is not meaningful as a biological concept because humans don't fit into neat little boxes marked "white," "black," etc. There is more genetic variation within groups than between groups, and this extends well beyond skin color or physical appearance. Race is a social construct.
This brief article explains things better.Of course, there are plenty of "white" or light-skinned Muslims, so Beet's assertion there falls flat on its face.