I would guess that airside originated from the days when the immigration check-point was the dividing line.

Once you clear immigration, where is some countries they stamp your passport; you have effectively left the country and are therefor "in the air". That is why you can buy duty / tax free goods.

In SIN and in the LHR where I have had plane going tech and have had to go back landside for an overnight stop, my passport has had to be re-stamped as having re-entered the country.

Nowadays, security check-points would be more appropriate as the reference point if they come before immigration or where there are no immigration checks; like domestic or schengen area waiting zones.