In other words, strictly a holiday for nerds, and has nothing to do with the mammal that lives mostly underground, including under the surface of our lawn, at times, except that it's OK to use mole, in any sense, in puns.
Here's a web page on the history of National Mole Day.
There's a National Mole Day Foundation. You can join it, by paying moledues.
There's at least one page of Mole Day jokes. Sample: "molearchy
- government in which moles are in complete control; under this government
Mole Day is celebrated three times a year and chemistry is the only scientific
subject taught in school"
Happy Mole Day!