Also that means that Lomography created a 110 square frame cartridge which is not compatible, if I get it right, with all the 110 cameras already existing.
If they had produced a "non pre-flashed" 100 cartridge the same cartridge would work on all cameras.
Thinking about it, this has to do with the "registration pin".
If a 13 x 17 mm camera mounts a 13 x 13 110 cartridge, and it uses the "registration pin" for film advance, the result is going to be a disaster in any case because a 13 x 13 110 cartridge will have its registration pins at a distance slightly above 13mm while a 13 x 17 110 cartridge will have them at a distance slightly superior to 17 mm.
13 x 19 cameras were probably designed to ignore the registration pins, I guess.