Few if any serious games were ever written in BASIC. The problem was you couldn't prevent anyone from looking at the program and cheating or making unauthorized changes to the game. So a lot of simple hobby games were written in BASIC but few games that you could buy were written in BASIC. In this time period, assembly language was king. There wasn't any C++ and K&R C was still evolving.
As the speed of computers increased, even interpreted BASIC started to become fast enough for simple graphics. You could effectively write a program similar to the original version of Wolfenstien in BASIC. If you can find it in the archives, I know of a simple maze/ray tracing program that could be modified to do something similar to this. It would be a lot of work though and you wouldn't be able to do any real fancy graphics. At this stage of things, you can compile BASIC into machine code though it still isn't as fast as C while C++ is starting to evolve. Assembly language is still at the heart of any serious games.
In the modern world, the game engine is probably still written in assembly language. You'll probably still find C behind some games but C++ is likely the dominant programming language. While C++ is the better choice for the huge environments modern games create, it still isn't as fast as well written C or assembly. There may even be one or two shockers around that are written in BASIC.
Several hobby type game programs are still written in a variety of programming languages. Python is one popular language. Java has been used for games as well. The choice of programming language for individuals is more often what they know rather than what might be the better choice for a given idea.
This covers the space of about 30 years or so. In the late 70s personal computers were slow. A simple text based game written in BASIC would sometimes pause while it sorted out it's response. As things progressed, in the late 80s, things got a bit faster and computers evolved. In the late 90s, we were starting to get better graphics and the video cards started to allow higher density graphics. I don't need to say much about the last 10 years as we are closing in on lifelike resolutions and movement in video games and this requires incredible speed to draw "cartoons" that fast in real time.
Shadow Wolf