I figured out why SpaceEngine won't run under wine. SpaceEngine creates a non-core OpenGL profile using wglCreateContext, but then try to compile GLSL shaders with "#version 330 core", which fails under Mesa GL.
I did some hacking to redirect the call and now it works fine on my machine. In theory, forcing a GL version using MESA_GL_VERSION_OVERRIDE should work, except there's a bug in Wine which causes it to crash.
BTW, if you are having crashes in openal32, just delete the openal32.dll file.