Greek manliness started from a different place than ours does now. For the ancient Greeks, it would have been incomprehensible to count yourself an alpha male simply because you can run a trading floor or sell an apartment because you gilded a faucet handle.
For them, real men defended or served their city, or performed some noble public service. Braying after money was the opposite of manliness. For the Greeks, that was just avariciousness, an activity that shrunk you down into a people-pleasing marketer or hollowed you out because you pursued hollow things.
The Greeks admired what you might call spiritedness. The spirited man defies death in battle, performs deeds of honor and is respected by those whose esteem is worth having.