Are these board games considered as gambling games?
I am not a lawyer, and have experience only in Ontario, but under Ontario law wagering on games of skill is not gambling. In a well-known case from the 1960's or early 1970's, in which the St. Clair Bridge Studio was defending itself against charges of running a gambling house, barrister and bridge player Eric Murray in his winning defence argued that bridge is a game of chance only as played by the justices of the Ontario Superior Court, in chambers. This despite the obvious fact that there clearly is a substantial element of luck in the cards dealt to each side on every particular deal.

As all of Chequers, Othello and Four in a Row are games with absolutely no element of chance whatever, and perfect information, under Ontario Law I believe none of them would be regarded as games of chance for which wagering would be prohibited.