Carmack is amazing at computer graphics and related technologies, but I fail to see evidence of the other two areas. He's never been much of a businessman - he's always focused on the technical side and left the selling/operations to others. I'm not aware of much he's done in terms of educational explanations, and the talks of his I've seen have been rambling and convoluted (but fascinating!).

I would recommend that you listen his recent podcast with Joe Rogan. He's such a great person altogether. Regarding business, I would not say he's only a technical guy. In the podcast he explains how he came to give his first Ferrari as the prize of the first Quake competition. He also explained (somehow to your point) how his rocket company failed.