How is he within scope? At best he might have contributed to advancing engineering science, but is that really the case? Has he not rather merely financed engineering science and perhaps not even engineering science but just engineering practice?

From the blogpost: "wider contributions to science, engineering or medicine through leadership, organisation, scholarship or communication" He's clearly relevant based on contribution to engineering (maybe science too) through organization (maybe leadership, communication too).

This is the salient point. Musk is not a "science" person. He is no Einstein or Newton. He has many good qualities, amongst them a broad appreciation of engineering, commerce and motivating people. He is ambitious. But Musk neither holds a PhD (I imagine he'd lack the patience and focus) nor has any notable specialism. Like Gates and Zuckerberg who both dropped out of their computer science degrees to make money, Musk is another of this new breed of "technologist" who we lionise as though they were "great scientists".

The Royal Society is a club for great scientists and it has erred by expanding its definition of "contribution to science" to include businessmen and financiers who contribute through money and influence.