The CHSH inequality was presented in the paper Proposed Experiment to Test Local Hidden-Variable Theories published in 1969 by J.F. Clauser, M.A. Horne, A. Shimony, and R.A. Holt. I'm interested in which paper first presented their proposed experimental apparatus in nonlocal game format, presumably also introducing & defining the concept of nonlocal games in general.
As far as I have been researching from the intrenet about the CHSH game, the first experimental realization seems to be the one published by Aspect in Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities. The experiment is based on photon polarization and is the proof of the universe's nonlocality at subatomical particle level.
About the general description of the non-local games I have tracked the paper Consequences and Limits of Nonlocal Strategies by Cleve et al. as the first formal description of those, and the CHSH game. I am not completely sure that this might be the first paper defining such concepts, but I think that is really one of them and it is a really good article concerning such topics.