The difference seems to be two-fold. First, Jaycar didn't go through an insane expansion (there are only 12 or so locations per state). Second, they've grown "out" from their core market of electronics hobbyist instead of betraying it. Just a few examples: custom car stereos, solar panel accessories, camping/RV electronics, boating electronics, and DJ-stuff like laser projectors. This is all in addition to the arduino and 3D printing stuff that you'd expect. There's a huge amount of cross-over between these markets, which works out great for Jaycar.
There is one additional factor keeping Jaycar healthy that probably shouldn't be underplayed. Due to mining and a less crypto-facist view of unions, Australia has not (yet) completely gutted it's blue-collar market and culture. Jaycar advertises almost exclusively to this "tradie" (as the Australians call it) demographic. Jaycar is marketed as a "manly" thing, not a "nerd" or "tech" thing. In fact, it's even drummed up minor controversy from feminist as being exclusionary with ads focusing on "leaving her to go to your man-cave" and whatnot. This part of Jaycar's success probably can't be replicated stateside. The market of people who have the skills to fix a small electric outboard motor and can still afford one died with the rest of blue-collar culture and jobs.