How is gender and race at all relevant for this joke?

The story itself isn’t a joke. The linkedin salesman guy wrote a stupid story about an unrealistically obnoxious rich guy who trips over his own racism.

How is that picture appropriate for a professional networking site?

Maybe he’s targeting people who look like that. The [guy who is rude to my target demographic] is quietly pwned by [my target demographic] (Now they will buy my product).

Also, what did the dude google to find that picture?

Ask him? His name is on the image.