While this site doesn't provide GIF conversion at the moment, you can
still do it yourself with the help of asciinema GIF generator utility - agg.
Once you have it installed, generate a GIF with the following
command:
agg https://asciinema.org/a/566180 demo.gif
Or, if you already downloaded the recording file:
agg demo.cast demo.gif
Check agg --help
for all available options. You can change font
family and size, select color theme, adjust speed and more.
See agg manual for
full usage instructions.