I don't think there is enough information to know. In particular ... who is the other player? Is it someone in their group, another group, a confederate or a computer simulation?
If the scores are of someone else in the study you have dyadic (or possibly more complex) data that will be very fiddly to model - and might require you to change the unit of analysis to dyad (or whatever) from the individual.
If the scores are not of someone else in the study then it may be simple - assuming the other play isn't confounded in some way with a varible in the model. Perhaps use the sum or proportion (or probably both) of critical comments as the DV and use mixed ANOVA to look at the critical comments by group and game (this might be as simple as a 6x3 mixed ANOVA). Ideally, you might derive a priori contrasts and test these in place of the standard ANOVA - if you have good theory to predict effects of interest.