I didn't see a gauge listed either. It seems like this is more of a tutorial than a specific pattern (although you do, of course, end up with a pair of socks in the end). Two sizes are given and are meant to fit a wide range of foot sizes.
If you want to use this pattern/tutorial, you could think about measuring your gauge
using the yarn and needles you've chosen to see how big your end result will be and then judge which of the two sizes seems most appropriate for you.