I used to wear drawstring waist loose woven boxers as a teenager in the Eighties and Nineties, but these were made for the domestic Chinese market long before tastes and local production become remotely westernised. I have not seen a pair on sale in the west in my life, although it's possible I still have some from my teenage years being used as dusters somewhere!
The kind of underwear you've described - seamless things made from stretchy fabric - do exist, but are rare on the High Street. They are more likely to be marketed as for sports; I seem to remember some at TK Maxx under the Head brand, but this was the best part of ten years ago.
You might be better off looking on places like eBay for "seamless underwear" being sold from Chinese traders. I've just had a quick look and "G3" or "G3Ltd" brand seems to be the kind of thing you're looking for. These are not, with the best will in the world, going to be items of quality though.
Other suggestions: some pyjama shorts are drawstring waist so a well-fitting pair might make a substitute for loose boxers. Or, find some underwear with covered elastic, remove the elastic, add your own drawstring and re-sew the top couple of centimetres over it.