If we were to replace electricity with gas it would be possible. Pressure and Flow of gas would replace Current and Voltage in electrics, and in most cases can be used for the same purpose.
As a worked through example (that is also very relevant as would be required as the basis for logic circuits), it should be possible to replicate a transistor by using some kind of normally closed diaphragm such that when a pressure is applied at the gate will allow flow from the source to the drain. This is exactly what a transistor does, though by using other physical effects to prevent/allow flow through the substrate. Transistors nowadays for the basis for logic systems, so now we know we could have valves and basic control systems.
Other fundamentals of electrics could be replicated. Resistors are replaced with orifices, capacitors with accumulators (though there are some differences here). Inductors are more tricky. Transformers can be made by enlarging/shrinking the cross sectional area of the flow.
So what's stopping it from working? Well scale would be the first issue. Transistors are tiny, even supposing we could somehow use pipes as small as carbon nanotubes, we probably still couldn't make something to work on the same scale. Sorry steampunk fans, wearables based on gasses are a little way off at the moment.
The next issue that one fundamental difference between gas and electricity for this sort of stuff is that an open loop in electricity is safe, whereas an open loop in your gas circuit is not safe. At best all that will happen is you'll lose a lot of gas and cripple other systems nearby (can be mitigated by logic to pick up massive pressure drops and shutting off the system). At worst that will meet one of your gas lamps and go boom.
One final issue is that there is a reason we use hydraulics instead of pneumatics for large machinery. Compressible gas doesn't give you nearly as good control as an incompressible liquid. Your rams would be springy, and would move as the load changed. If there was something preventing something in the system moving, the pressure would build up til it could overcome the obstacle, then would suddenly jump. It's not the smooth control you need for a lot of purposes, but just opening closing valves could work.