When it comes to Gambas, there are two general approaches.
- Making games within the graphical toolkits, most notably Qt 5 though GTK 3 is supported, using pictureboxes or drawing area controls (which I do)
- Writing all the rendering and multimedia using SDL (as several games on the Gambas Farm do)
For the first, I am probably the most prolific coder in this space, so if it does not seem too immodest, I could just ask you list:
As for the second, it is essentially similar to using raw SDL in C or Python or anything else. There are not any specific engines or libraries ala pygame that I am aware of. OpenGL (2.1 using the aged component, though 3 and later can be loaded externally) can be used from either an SDL window, or the graphical toolkits using a built in control (as my PS Tech engine does), to handle hardware acceleration.
In general though Gambas is a very centralized language, which is a strength and a weakness, so rather than having third-party libraries you use the built-in components provided.
As for free software BASICs more broadly, there are also SDL and Allegro bindings for FreeBASIC, and there is a dedicated SdlBasic (as well as a Basic4GL, though that uses the ancient OpenGL 1.1 specification). These build on from the once quite vibrant QBaisc game development community, which the QB64 compiler targets most directly. Again these mostly seem to be integrated directly to the languages. There are one or two game engines for FreeBASIC listed on GitHub though.
This might also warrant a look for the Pascal section: