DirectX is C++ (technically a set of COM interfaces) and most game engines are also C++.
Unlike, say, Linux programming where C is the standard, almost all games have been written exclusively in C++ for a long time now, probably three decades.
COM was designed to be compatible with C. Linux games are also often written in C++. The ones written in C are just old.
There are a few exceptions though, like most mobile games, visual novels (many of which use Python of all languages, due to an excellent framework called ren'py), and of course games written using Unity or XNA, which use .NET languages.
Also, three decades is going a bit too far back, I think. In the mid nineties, C was still king, with assembly still hanging on. C++ was just one of several promising candidates, with some brave souls even trying Java.