How to set up z-buffer instead of OpenGL or DirectX?

Question

linux

Let's start with the fact that I installed Debian on my Asus ZenFone 2 ZE551ML via LinuxDeploy. In a Linux container, I installed libgl-mesa-swx11 (for 3D graphics) and wine. Everything works fine, except... I ran Deep Exploration, opened a simple 3D model, and chose between different graphics modes (or whatever you want to call them), resulting in the following:
OpenGL gave 1-2 fps
DirextX gave 1-3 fps
Software z-buffer gave out 12-18 fps
And now I have a question: is it possible to somehow use z-buffer instead of opengl and directx for other games / programs that only give you a choice of DirectX and OpenGL? For example, in Half Life you can choose both OpenGL and DirectX, but I would like to choose z-buffer and feel the increase in fps.
I’ll say in advance, there’s no need for complex terms, just tell me if it’s possible and how ...