I have an open source XNA/MonoGame implementation of a similar lighting technique available here:
https://github.com/sq/Illuminant
It's hardware-accelerated and has a few other useful features; we're using it in Escape Goat 2 and it works on Windows/Linux/Mac on pretty much any D3D9-spec hardware. You can see some of the levels using it here: https://www.youtube.com/watch?v=-9s1PyotS18#t=1m20s
For EG2 we have a pair of separate lighting environments; one for the foreground plane and one for the background plane. Most light sources exist on both planes but have different parameters in order to create a depth effect; some light sources are only on the background plane. We apply a customized ramp texture to the light sources in order to replace the smooth attenuation with quantized attenuation, and we don't use soft shadows (though we do render lighting at a lower resolution and upscale it, because that softens things a little.) We also do a simple HDR camera model by sampling lighting intensity across the scene's foreground/background planes and using that to adjust the range of the final lightmap so that we can automatically tune exposure/white point etc to highlight certain parts of a level.
I also have a similar pure-software-rendering lighting library from around ~8 years ago available here, in C++:
https://github.com/kg/Fury2/blob/master/libraries/SoftFX/mod...
That one's garbage, but may still be of some use.
I'll note that the author's approach (needing extra intersection points at +- 0.00001 radian) is a little perplexing. I'm not sure why that is needed; I've never needed it.
A better approach for 'fuzzy' shadows is to model the penumbra; you can render it as a single triangle that borders on the actual shadow umbra and then make it smooth by using a simple lookup texture. This technique is described here:
http://archive.gamedev.net/archive/reference/programming/fea...
Another great option for 2D lighting is to associate normal maps with your sprites and do per-pixel lighting against each light source using the normal map. This can produce some really great results. I think that SpriteLamp, http://snakehillgames.com/spritelamp/ does this; the Fury2 library I linked above also did per-pixel sprite lighting with normal maps. The upcoming game Full Bore (http://www.wholehog-games.com/fullbore/) is using per-pixel lighting on its sprites and environment art, and I believe Spelunky for PC/XBLA uses it on environment art.