That was a state house of representatives seat, one of four hundred NH state representatives. In the 2016 general, a D missed the seat 1,960 to 1,667 (it's a multi-seat district, but if we look at just those two, it was 54%-46%,) in the special, the D won 811 to 755 (52%-48%.) A 6 point swing is nice and Ds should take encouragement from it, but it's such a small sample (even including the NY state assembly seat that also flipped) it's not a reliable indicator of a sea change. The 6 point loss in the MT US House race is a much better indicator.
Don't discount the candidate effect either, the D in this NH race was a lifelong resident and executive director of area non-profit, the R was a lawyer who had recently moved to NH from VA.