Why does the romanization Mahjong have a final H after ma? What romanization system of what language or dialect is this from?
I've seen no other romanization of Mandarin or other Chinese languages or dialects use a final H.  

Or may it be just common english-speaking use to avoid being pronounced may-jong?
Refer to Mahjong In The West

I think it is just a translation problem.

In the old times, romanisation in Chinese Language like Cantonese Romanisation is not really common, like in this case, Mahjong might be translated from the Wu Dialect or Northern Chinese Language, I'm not sure about that.

You might also refer to this The Mahjong Origin

I hope I did answer your question. :)