If I wanted to make a homemade alcohol drink from figs, I'd either steep chopped tastey figs for a couple months in good vodka or everclear as Suzi suggested (where can you buy everclear in California?) Much as you can make Limoncello at home from fresh lemon peel, sugar, and vodka.
Or... ferment figs - crush, add some yeast, perhaps some sugar if your figs arent that sweet, and ferment them like you would grapes for wine. You can do this in a container with a narrow neck. For a vaporlock, you can stretch saran wrap over the top, secure iwth a rubberband, and prick it with a pin. You want the carbon dioxide to escape, but not let oxygen in. Then let it bubble away. This works quite well for fermenting apple juice from the store. Don't ask how I know. :)
You also want to add yeast as mentioned. But not bread yeast or it will taste bready. Find some champagne yeast on ebay. It's not all that expensive and is supposed to make a good product. I forget all the reasons why.
The Figenza site said it was triple distilled, which perhaps means they took their fermented fig concoction (wine) and 'cooked' off the alcohol in a still (low heat, copper kettle and coil) and caught the alcohol and put it into a fancy bottle. Like moonshine, or vodka, only probably far more sophisticated. Lol, or maybe not. :)