My 2 cents...
My very first job was working in a screen print shop. We would use puff ink all the time and I've mixed inks that that have given the same look. We would use a base color (in this case a charcoal grey) add some metallic powder and a puff additive. The puff additive was activated when you ran the item through the dryer... as in a screen print dryer. Like a 10-12 ft conveyor belt oven of sorts. When your print came out the other end it was puffy and cured. that's all I got.
EDIT: Also thinking the screen emulsion was nice and thick some when they laid down the puff ink it was equally as thick. (maybe?)