When I was growing up, my mom would call them VTVMs, well after they started to be built with transistors...
(Vacuum Tube Volt Meter)
I don't think that it is fair to say that the device measures current, even if the mechanism by which the meter _indicates_ is because of current flow. There are any number of mechanisms by which the quantity that you want to measure can be converted into a quantity that is easy to perceive, and current creating a magnetic field and acting against a spring is but one of these.
Voltage can be measured by the direct physical attraction of the electrostatic field, eg. in some forms of oscilloscope, or electrostatic action against a spring.
Current can be measured by its magnetic field, or by voltage induced in a magnetic field (hall effect), or by the temperature change of a resistor.
I am certain that there are other mechanisms.
Understanding the mechanism that a particular measurement instrument uses is very important, because it help to understand what other influences will corrupt the measurement.
-Jon