in game analysis - why an inaccuracy?
Anyone who uses penultimately correctly deserves a response.
The computer just follows rules that a human created. A human said, "If you evaluate all the moves and then played move is worth X points less than the highest-valued move, then mark it as an inaccuracy. If the differences is more than Y points, call it a mistake."
You have several decent moves at that point. 10. Qxg4 would have been harder for black to deal with.
10. Bd3 Qb6 gives the king an escape route and possibly encourages you to exchange queens, both of which are good for black.
In that sense, Bd3 is inaccurate because with better play, black would have survived longer.

Bd3 is fine, it attacks the N twice and threatens #. Moving the Q saves the # but the N's had it and white's easily winning. It's an inaccuracy though because there are stronger ( but more complex) moves such as Qc5 which piles on more pressure and wins more material ( although not immediately) Bd3 is probably best for most people though as it is simple and still a winning move.