Edit: I'm using the GL enum, which is incorrect since it's not part of OpenGL ES (see my answer). I should have used GL10, GL11 or GL20 instead.

Here's a few snippets of what I have so far...

void create()
{
    renderer = new ImmediateModeRenderer();

    tiles = Gdx.graphics.newTexture(
        Gdx.files.getFileHandle("res/tiles2.png", FileType.Internal),
        TextureFilter.MipMap,
        TextureFilter.Linear,
        TextureWrap.ClampToEdge,
        TextureWrap.ClampToEdge);
}


void render()
{
    Gdx.gl.glClear(GL10.GL_COLOR_BUFFER_BIT | GL10.GL_DEPTH_BUFFER_BIT);
    Gdx.gl.glClearColor(0.6f, 0.7f, 0.9f, 1);
}

void renderSprite()
{
    int handle = tiles.getTextureObjectHandle();
    Gdx.gl.glBindTexture(GL.GL_TEXTURE_2D, handle);
    Gdx.gl.glEnable(GL.GL_POINT_SPRITE);
    Gdx.gl11.glTexEnvi(GL.GL_POINT_SPRITE, GL.GL_COORD_REPLACE, GL.GL_TRUE);

    renderer.begin(GL.GL_POINTS);
    renderer.vertex(pos.x, pos.y, pos.z);
    renderer.end();
}

create() is called once when the program starts, and renderSprites() is called for each sprite (so, pos is unique to each sprite) where the sprites are arranged in a sort-of 3D cube.

Unfortunately though, this just renders a few white dots...

I suppose that the texture isn't being bound which is why I'm getting white dots. Also, when I draw my sprites on anything other than 0 z-axis, they do not appear -- I read that I need to crease my zfar and znear, but I have no idea how to do this using libgdx (perhaps it's because I'm using ortho projection? What do I use instead?).

I know that the texture is usable, since I was able to render it using a SpriteBatch, but I guess I'm not using it properly with OpenGL.