Why is gas pressure measured in mmHg?
History and because of how pressure works

The original reason why mm of Hg are used is because of how chemists first started to measure and understand atmospheric pressure. The idea of the vacuum and atmospheric pressure is surprisingly new. Otto von Guericke demonstrated the power of atmospheric pressure by showing that two horses could not separate a brass sphere containing a partial vacuum only in the 17th century (remember a vacuum doesn't suck the atmosphere pushes). 

This kicked off a vast amount of experimentation. Around the same time scientists like Torricelli and Pascal realised that they could measure atmospheric pressure by filling a closed tube with mercury and inverting it in a bath of mercury (you can do this with any fluid but mercury is about 13 times denser than water so the tube only needs to be a meter or so long; with water it needs to be ~10m long which is an inconvenient length in an indoor laboratory). The height of the mercury in the tube is a measure of the external pressure as a vacuum is formed above it in the closed tube. This simple instrument was used by a friend of Pascal to show that atmospheric pressure drops with height when he took a barometer up France's Puy de Dome mountain.

The diameter of the tube is irrelevant as pressure is weight/area (do the calculations and tube diameter cancels out).

We now call a tube like this a barometer. And the height the mercury rises to is a convenient measure of atmospheric pressure and can be read off using a simple ruler. We could use mm of water, but would need a much longer tube and an unusually inconveniently sized ruler. Hence why mercury is the fluid and a convenient way of measuring pressure is mm of Hg. 

We tend to use modern SI units for pressure these days, not least because the wide use of mercury has been banned and calculations in consistent nits are far easier.