Dimmer with ungrounded box

Question

I have a new Legrand dimmer switch. It has a connection for a ground.
However the box it needs to go into appears not to be grounded.
The dimmer is model LSCL453P.  The load is an LED light about 30 watts.  This is not in an office (not bathroom or kitchen).  The switch cover is plastic.
The voltage between the two wires is about 100V AC. The voltage between one wire (left in the picture) and the box is about 50V AC. The voltage between the other wire and the box is about 40V AC.
    
Is it going to work ok if I just connect the two wires?
Is that going to be any less safe than the alternative of just putting back the old on-off switch?

Edit:  Some more investigating, it seems that the box is at about 40 volts AC relative to ground.  So the basic premise of the question ( that the box is not grounded) is correct, but not in the way I assumed (i.e. that the box is not electrically connected to anything else in the world).  I fear this has gone beyond a DIY project and calls for on site help from a qualified electrician.
Another edit. Putting an ammeter between the box and a trusted ground gives 0.2mA at about 40V.   Resistance between the box and a trusted ground is very high. So I'm fairly sure the 40V is a parasitic voltage caused by capacitative coupling (and maybe some inductive coupling too) between the BX armour and the hot wire running through it. Likewise, past a certain point everything else on that circuit that should be grounded isn't. So now I'm back to where I started. The box simply isn't grounded. The lesson for me is to check both the voltage and amperage against a trusted ground.  Just for safety's sake, not to mention getting the dimmer to work, I'm going to ensure that everything that should be grounded is.

Harper - Reinstate Monica · Answer

If it's there, the switch will pick up ground via its mounting screws.
The rule of grounding is if there's a metal  box, the wiring must ground to the box as its first priority. Ground to the box first, only then have pigtail grounds to receps and switches if they're needed (which they're not on switches; certain receps need that).
Keep in mind, some modern dimmers require a ground to perform properly.  They have gotten permission from UL to use ground as a current return, because their device inherently will be leaking too little current to possibly matter, and has internal safeguards so no foreseeable damage or failure will cause more.  The upshot is that if ground is no good, the device might not function.
I agree that it looks like metal conduit or possibly AC cable, which provides a ground path to the box. (and again the rule is "must ground the box first").

Ed Beal · Answer

The OEM instructions say to use the green grounding screw.
With that said it is irrelevant if the screws are grounded.
My guess is that a small current Is dumped on the ground to make the dimmer function properly this is not unusual, if the box is grounded through a conduit the switch may work, if it is not grounded and the switch doesn’t work it is now legal to pull a new ground from an existing circuit or going back to the panel as long as the ground is pulled from a device fed from the same panel. If you only have a main panel you could tag any other circuit that was grounded and be code compliant.
I have run into a few of this style switch that uses the ground as a return for the switch. This is rated for small loads of cfl or led with 10w being the minimum load for proper operation.

Dimmer with ungrounded box

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