Boring Chess?

MY opponent at the conclusion of our game in round six of Bad Wörishofen U2000, accused me of playing boring chess and not being interested in winning.
Jochen Eilers (1974) - Spanton (1890)
French Defence, Irregular Variation
1.e4 e6
As well as calling my play in general boring, JE dismissed 1...e6 as "boring," saying he had prepared for 1...e5 and 1...c5.
2.Nc3 d5 3.g3!?
There are more than 500 examples of this move in ChessBase's 2019 Mega database, and it was not a surprise to me as I knew JE was fond of fianchettoing his king's bishop when playing 1.e4.
3...d5xe4 4.Nxe4 e5!?
A suggestion of the analysis engine Stockfish10. The justification for moving the e pawn a second time is, presumably, that White has spent time opening two diagonals for his king's bishop, so Black has time to grab space in the centre.
5.d3 Nc6 6.Bg2 Nf6 7.Bg5 Be7 8.Nxf6+ Bxf6 9.Bxf6
I thought White's idea was 9.Bxc6+!?, doubling Black's c pawns, followed by 10.Bxf6 to remove Black's resulting bishop-pair, but JE said he did not think it was good to give up his king's bishop in this way.
9...Qxf6 10.Ne2?!
My main analysis engines do not like this, preferring 10.Qd2 (Stockfish10) or 10.Qf3 (Komodo9).
10...Bg4 11.h3 Bxe2?
Missing  the strength of 11...Bf3, eg Stockfish10 gives 12.Bxf3 Qxf3 13.0-0 0-0-0 with a strong attack. If 12.0-0, then Stockfish10 gives 12...Nd4 13.Re1 0-0-0 with what it reckons is a winning attack.
12.Qxe2 Nd4 13.Qd2
13.Qd1!? looks retrograde, but unbalances the game somewhat by preserving the bishop, and it eventually becomes the engines' choice.
13...Nf3+ 14.Bxf3 Qxf3 15.0-0 0-0-0?!
I probably should have played the safely centralising 15...Qd5, rather than offer a pawn, or pawns, for speedy development.

How should White continue?

*****
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16.Rae1
Critical is 16.Qa5 Kb8 17.Qxe5, when Black does not seem to get enough for the pawn(s), eg 17...Rde8 18.Qxg7 Reg8 19.Qh6 Rg6 (19...Rxg3+?? 20.fxg3 Qxg3+ 21.Kh1 Rg8 22.Qd2 Qxh3+ 23.Qh2 wins for White) 20.Qd2 Rhg8 21.Kh2 Qh5 (what else?) 22.Qe3 Rh6 23.h4 (or 23.g4 - Black's back rank is weak). Another possibility is 17...Rhe8 18.Qxg7 Re2 19.c4!
The engines give Black's best as 17...f6, when after, say, 18.Qc5 Rhe8 19.Rae1 Re2 20.Rxe2 Qxe2, Black has some pressure for the pawn.
16...f6 17.Qe3 Qxe3 18.Rxe3 Rd6
The engines come to like 18...g5 to discourage the 19th move played by White in the game.
19.f4 exf4 20.Rxf4 Rhd8
JE now played ...
21.Rfe4
...and offered a draw, which I immediately accepted. The engines reckon White is slightly better after a move such as 21.Kf2, 21.Rh4 or 21.Ra4.