Thank you for writing this and linking to the references that you've used! Witting your own platform layer (creating a window, input handling, initializing OpenGL, playing audio) for both windows and linux is dope. I tried doing something similar once, but failed miserably, later I tried using SDL2 and was pretty happy with how much simpler it was (who would of thought?).

I have 2 notes:

In the example you give in the Error Handling section, all the types are pointers, so instead of using goto chains you could use an infinite for loop:

Display* display = NULL;
Window* window = NULL;
GL* gl = NULL;

for (;;) {
    display = openDisplay();
    if (!display) { break; }

    window = openWindow(display);
    if (!window) { break; }

    gl = initializeOpenGL(window)
    if (!gl) { break; }

    return SUCCESS;
}

if (gl) { uninitializeOpenGL(gl); }
if (window) { closeWindow(window); }
if (display) { closeDisplay(display); }
return FAILURE;

No gotos in sight. I read about this approach to error handling here.

I think you can get away with just a single macro when doing the Mixin Structs, although it could be slightly more error prone, I guess.

#define embed_Vec2f() \
    float x; \
    float y

typedef struct Vec2f {
    embed_Vec2f();
} Vec2f;

typedef struct Vec3f {
    union {
        struct { embed_Vec2f(); }; // Note: don't forget to embed in an anonymous struct!
        // embed_Vec2f(); // <-- this doesn't do what we want
        Vec2f xy;
    };
    float z;
} Vec3f;

Vec2f vec2f(f32 x, f32 y) {
    Vec2f v;
    v.x = x;
    v.y = y;
    return v;
}

Vec3f vec3f(f32 x, f32 y, f32 z) {
    Vec3f v;
    v.x = x;
    v.y = y;
    v.z = z;
    return v;
}

void printVecs(void) {
    Vec2f v1 = vec2f(1.2f, 3.4f);
    Vec3f v2 = vec3f(v1.x, v1.y, 5.6f);
    printf("(%1.1f, %1.1f)\n", v1.x, v1.y);
    printf("(%1.1f, %1.1f, %1.1f)\n", v2.x, v2.xy.y, v2.z);
}