Cancer is an inherently evolutionary disease, characterized by a proliferative phenotype that is often able to evade treatment. This treatment resistance has inspired novel evolutionary therapy techniques aimed at improving patient survival by delaying or avoiding pervasive multi-drug resistance. Across most proposed evolutionary therapies, we require a deep understanding of tumor evolution alongside a sufficiently predictive mathematical model to inform therapy scheduling. One key factor in accurately modeling tumor evolution is incorporating the interactions between multiple cell types. Averaged over the population, cell-cell interactions produce frequency-dependent fitness effects that can result in divergence between measured monoculture growth rates and co-cultured dynamics. Novel in-vitro bacterial and tumor studies have used experimental game assays to validate the presence of these interaction effects directly. Of particular interest to the development of evolutionary therapy is mounting evidence that these cell-cell interactions change with drug type and concentration. We aim with this work to improve the modeling of drug-dependent cell-cell interactions and to explore interaction dynamics as a modification of monoculture growth dynamics. Modeling cell-cell interactions is often carried out using evolutionary game theory and the replicator dynamics. In the two-player replicator game, the possible evolutionary stable states are well-understood, and classified into four quadrants or game types. Motivated by pharmacodynamic experiments and potential growth-rate dependency of cell interactions, we decompose the two player payoff matrix into cell-intrinsic and cell-extrinsic terms. Using this framework we analyze experimental game assay data from co-cultures of ancestral and engineered mutant (EGFR, BRAF) NSCLC cell lines to analyze the drug-dependency of cell-extrinsic and cell-intrinsic growth effects separately. In addition we unite existing pharmacodynamic modeling with game interactions, proposing various simple mathematical forms for the cell-extrinsic interaction term based on a simple range of mechanistic hypotheses. We show that a linear growth-rate-dependence of the extrinsic interaction can result in non-linear traversal of game-space with drug concentration and can traverse multiple game types with changing drug concentration. Our biologically inspired game theoretical formulation for cell-intrinsic and cell-extrinsic opens up an avenue for modeling of game interactions and ecological effects. We use it to explore drug-dependence of these factors in models and experimentally derived evolutionary games. This work demonstrates a new biologically meaningful framework for evolutionary games, a framework for mechanistic hypothesis testing and unites game theory with traditional monoculture experiments and pharmacodynamics.