A lightning strike creates a magnetic field with a high rate of change which induces voltage into any loops made of conducting material. It works like a transformer. The primary coil of this transformer is the lightning bolt itself, and the secondary is any cable loop in the vicinity.
In this case the cable loop could be something like:
Mains - Switch power supply - Ethernet switch - Ethernet cable - Desktop PC - Mains
...but really, any cable loop will be hit with induced voltage, which means devices which are at the intersection of several networks (electrical grid, telephone, cable TV, ethernet, etc) have a chance of being part of these loops.
The larger the loop (in terms of surface area) the higher the voltage. So the loop created by two twisted wires inside a cable receives a very small voltage because the wires are close together, whereas the example loop above will receive a much higher voltage, because the cables involved can be far apart.
It is not possible to prevent this induced voltage from happening when lightning strikes. What the protection device does is provide an easy path for the surge current to flow, so it flows through the protection device and not through the sensitive device it's supposed to protect. The usual way is to use a TVS diode or other voltage limiter between the wire to be protected and the Earth conductor.
In the example loop above, if the devices are equipped with surge protectors this means the loop becomes:
Earth - Switch power supply - Ethernet switch chassis - TVS - Ethernet cable - TVS - Desktop PC chassis - Earth
So the current goes from the cable through the TVS, the chassis, then Earth, and closes the loop through Earth back to the cable. In both cases it doesn't go through the network interface chips at both ends of the cable.
However the surge protector in the question doesn't have any connection to Earth... so the only thing it can do is protect against high voltage between the wires in the Ethernet cable (which never happens) but it can do nothing against high voltage between the cable and Earth. So it's going to be completely useless.
This has nothing to do with the shield on the cable: without a connection to Earth, a surge protector can't sink the surge current to Earth to protect sensitive devices.