One good solution is to create render target of double size, calculate coordinates for ends of line, instead of line render quad of width 2, and then scale down to screen size. This is called supersampling (oversampling).
Take note that in that example A, B, C are vectors, HGE has hgeVector type which can do those operations, vector minus, vector dot product (cross in the article), vector set length (hgeVector Normalize and multiply by length).
Take note that you don't need to draw 2 triangles in HGE, as HGE has hgeQuad class which draws a 4-cornered polygon for you.
P.S. I assume you can read examples and documentation and figure out how to use hgeVectors and draw a hgeQuad.
Also write your game without smoothed lines, there are many more problems ahead :) You can't just stop here because HGE doesn't draw smoothed lines.