Tim,
WD has the ability to create static mesomaps, up to three of them, as noted in this FAQ:
However the station markers would not be the same as what you pointed to. The map you linked to appears to be based on data from WU and NOAA only and may be provided by WU, not sure…
There is also some other Mesomap scripts out there but most are for fee scripts and I really haven’t paid much attention to those…
BTW just for fun type “mesomap for website” into google and see what the top almost 10 results point to… MML 
-Bob