The way people enjoy a drink nowadays is different from the way it was used to be done, as I'm sure you can imagine. Certain liqueurs were drunk pure and without ice. The glass could be chilled by swirling an ice cube in it, a process called 'frapper' [frappay].
In french these small glasses, shallow or not, for liqueurs are called 'verre à gouttes'. I think i might have mentioned this before elsewhere. A 'drop' glass, as the quantity per glass is so small. The expression still exists today when people offer eachother a drink by asking 'une petite goutte?'.
I'm not suggesting they are of french manufacture, only just highlighting the fact that they are liqueur glasses which you understood anyway
