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Is King's gambit really an inaccuracy

As far as I know, what is defined as an inaccuracy in the computer analysis is strictly related to how Stockfish evaluates the position relative to the best available move, so it’s literally just based on the numbers the Stockfish algorithms crank out. It’s not a value judgment or anything. Stockfish just doesn’t like it.
Kings gambit has been proven to be a draw after exf4. The only drawing move is Be2.

However, that's no reason not to play it!

Also, your opponent really misplayed the KG although I'm no expert myself. Nf3 is the most common third move but Bishop's gambit with Bc4 is playable. g3? Ew...
I had a strong engine (3000+) play kings gambit against itself 3 games in a row at full strength.

1/2 1/2 1-0

White scored 2/3 points.

So if the engine can draw, and win with it at high strength I think it can't be that unsound.
The white's third move is very weak. It's explain your absolute victory.
No Fischer called 3 Nf3 weak and called 3 Bc4 the only correct move. He played it himself with success.
In the TCEC 2016 Superfinal Stockfish 8 played Houdini 5. Both engines agreed on -0.50 disadvantage for white, but both engines won their game with white against one another.
the opening is fine. humans arent perfect.

as for inaccuracies and mistakes...

try the halloween gambit (which has more problems for white, but I love the opening and play it)... sometimes the engine will say its an inaccuracy and sometimes mistake.

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