Electrical sub panel grounding
You have invisible grounds

Your building seems to be wired in conduit.  This is a very different wiring system than you're used to with cables.  This uses a conduit pipe laid to various destinations, and then individual wires laid in the pipes.  The individual wires are typically type THW, THHN, THWN or XHHW. 

You can tell because a) the wires have writing on them, b) the wire entries look like conduit, and c) colors are atypical of what is found in cables (e.g. blue wire). 

New work is often done in PVC conduit, but then, grounds would have been required.  The Zinsco panel certainly suggests it predates PVC conduit.  So my conclusion is this is metal conduit, which is a superior system you should be glad to have. 

The Zinsco panels, on the other hand, are a fire looking for a place to happen. I realize the panels are "built-in" and replacing them would be a chore, but at least look into Eaton's retrofit kits for Zinsco panels. 

Therefore your ground "wires" are actually in the metal conduit pipe itself.  This is a reliable and superior system.  Do not replace any segments of the metal conduit with PVC.