No. A manometer is referenced to a certain pressure while a barometer is referenced to vacuum. That is what makes the difference, not the type of measurement. Both can cover a wide range of precision.

Seems to be a mix of unprecise information by the manufacturer (engl. website states ‘barometer’; german website states ‘Manometer’) and poor research (GIZMODO states both).

...‘barometer, and even a manometer’...