That is certainly a perfectly valid way of defining something as a "portrait". It is a fairly traditional definition though, and there are other ways of defining portraits.
To pick an example from the painting world, I think that Diego Velazquez's – "Las Meninas" is both definitively a portrait, while still being much more than just a visual message.
And just about any of Jane Bown's famous portraits are enhanced greatly if you know even the slightest amount about her subjects - Samuel Beckett being a perfect example:
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