They are using smooth time integration, where I am using the discrete scheme described in the arxiv paper. The switch isn't that difficult though, since it just involves modifying a single line of the shader.

The SmoothLifeConfig.txt doesn't have a line for SmoothLifeL - it should, Stephan!

Here it is:

2 1 10.0 3.0 10.0 0.100 0.257 0.336 0.365 0.549 2 4 4 0.028 0.147 // SmoothLifeL

Put this at the top of SmoothLifeConfig.txt and run the exe.

You'll notice that some of the parameters (the 2 4 4) control the transition function. This is different to the version in the paper which is smoothglider (which is in the config file) which uses 4 4 4.