GP is correct that the argument contains an informal fallacy[1], and people often express this criticism by saying "your argument is tautological," and you are correct that a tautology is a statement which is always true [2].
> GP is correct that the argument contains an informal fallacy
The GP didn't say that.
As for which informal fallacy the GGP's argument contained, I would say it was more like a false dilemma. And the GGP did say "almost tautological", which implicitly recognizes that there might be other possibilities.
> people often express this criticism by saying "your argument is tautological,"
I have never seen this (nonsensical) way of expressing the criticism that an argument is false by saying that it is tautological (and therefore true).
[1] https://en.wikipedia.org/wiki/Begging_the_question
[2] https://en.wikipedia.org/wiki/Tautology_(logic)