How does equipment ground protects us from electrical shock?
Not quite.
In the case if the black wire touches the metal casing and a person is touching the case, then the ground wire would lower the return circuit resistance, causing a very large current to flow. This will blow the fuse in the plug (UK BS1363 plugs) or the much larger fuse or trip the breaker in the house circuit, keeping the person safe even before they touch the enclosure.
If the ground wire isn't fault current rated or the breaker is too high current for the circuit, a fire ensues instead.

In the second circuit, only a small current is required to kill the person. If the concrete floor provides a very high resistance, the person feels an unpleasant tingling but probably survives.
If they touch some grounded metal with the other hand, the current increases. Now the RCD (UK) or GFCI (US) can see current flow on Live which isn't balanced by current returning on Neutral, so it trips at 20 mA or so : unpleasant but not usually fatal.
(This may also happen in the first scenario : there's a race between the protection mechanisms. Older houses may not have RCD protection so fuses/overcurrent breakers are still a good idea)

In either scenario the person is protected IF the protection mechanisms are properly installed, tested and working.