(Really we should be talking about perfectly competitive games, and you could have a perfectly competitive game which has nonconstant total utilities, e.g. by taking a constant-sum game and then translating and scaling one of the utilities. But the above game is in fact not perfectly competitive; in particular if there’s a Pareto dominant outcome or a Pareto-worse outcome, assuming not all outcomes are the same, it’s not perfectly competitive.)
(Really we should be talking about perfectly competitive games, and you could have a perfectly competitive game which has nonconstant total utilities, e.g. by taking a constant-sum game and then translating and scaling one of the utilities. But the above game is in fact not perfectly competitive; in particular if there’s a Pareto dominant outcome or a Pareto-worse outcome, assuming not all outcomes are the same, it’s not perfectly competitive.)