They may work as dogs (although very loose in my bench), but I've always used similar to assist in finishing, especially restoration finishing. Great for control, when you don't want the finish to leak onto adjacent timber/contrasting cockbeading etc. Also for levelling fillers/softwax where the risk of scratching/scraping rules out metal implements.
Dobbing sticks may be a local term, although I've come across it in Scotland, Northumbria and Yorkshire.
I suppose only my Secret Santa knows what he make them as, but I know what I'll be using them as, and I thank him, they're great for it. =D>