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Calculating Two Moves Ahead

This is one of the games I am most proud of,
but something my dad said was very degrading.
He said that without error there can be no brilliancy.

It's a mate that relies on your opponent making those moves, so while it's great you found it because you played it perfectly (and kudos to you for that--really), I just wouldn't count on your opponents setting you up for that either.
Still, I don't fully agree with your Dad's phrase. For brilliant moves without major errors, I'd check out some grandmaster games. Fischer v. Spassky game 6 is a great example of no huge mistakes made, and yet Fischer made some subtle moves that gave him an overwhelming advantage.

Here's the lichess link to a good analysis of that game: lichess.org/video/d2WlFD2rbRk
"no huge mistakes made"

"overwhelming advantage"

Unless you think one side starts with a huge advantage, this makes no sense. I mean, sure, perhaps a computer won't call it a blunder by whatever arbitrary standard it is programmed to call things blunders, but just because a move is "subtle" does not mean it is not a mistake to overlook it.

If neither side made a mistake, then there is no way to have "an overwhelming advantage."
Whites f3 move was a dubious maybe even a full blown mistake followed by a really obvious blunder. Great game very instructive I learned a lot from this :D Looks like a game where I would have white in wrongfully so.
My dad was so envious that he vowed to study eight hours a day until he finds a mate in one.
Calculations are easy, every chess player can count.
It's the analysis of all possibilities that is harder to visualize.
Chess brilliancy is a wisdom that some chess players have to foresee a convenient combination in the horizon. It's like a star that shines in the dark and nobody else noticed it, until it was pointed out.

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