It feels wrong to me for the chairman to overturn votes cast, even though the constitution allows it.
No, giving the Chair your vote to use at their discretion is casting it. If the Chair simply followed the majority of defined votes, what would be the point? It would be the same as not voting at all.
I often give my vote to the Chair as a discretionary. I do so with the expectation that they will use it in line with the opinions of the board/committee, whether or not that coincides with the majority of defined votes. I did so in this case, I don't have particularly strong feelings either way, I'm doubtful it'll encourage many riders, but see no harm in it. It is a decision that might benefit potential riders, who have no say, it might also create some extra admin for the organisers, I was happy for the Chair to use my vote with a better understanding of the implications than I have. Whatever your opinion, it was my vote to cast and I did so.