But if you yourself want to write your own game with just you or a small team of like-minded people, I would highly encourage using C++. As long as you don't have too many cooks arguing about which C++ features to throw into the pot, you can pick a subset of C++ that isn't much more complex than C (which is already more complex than most realize) and you'll get a much cleaner, safer language. C++ has saner rules for implicit type conversions, namespaces, overloading, and a cleaner notation for dynamic allocation. Those alone make it a sufficiently "better C" to be worth using in my book.
Going farther, even if you don't like "object-oriented programming", I think classes offer modularity and encapsulation features that make them worth using, even if you never once write the keyword "virtual" or use subclassing. (Fun fact: the first version of C++ did not have virtual methods!)
I like C and enjoy programming in it, which I've done for over 20 years. I've written a successful open source project in it and am writing a book that uses C as one of the implementation languages. Even so, I generally only use straight C if I'm writing a library that I want C users to be able to consume. Otherwise, I think C++ contains any number of "better C"'s within it, and it's mostly a matter of choosing which better C you want.