No disrespect or insult meant, but this just demonstrates ignorance of what the issue is, and generally what the grounding lug on an appliance is for.
Notice that some things have grounded plugs some don't. Why?
Has absolutely nothing to do with the electronics inside. Indeed, the electronics SHOULD be completely isolated from the case electrically.
Appliances, with metal parts that can be touched by the user, are required to have a grounded plug, and the ground connection is supposed to be connected to the metal enclosure and any metal parts that are accessible to the user.
I'm an electrical engineer. Got my degree in '84. Been doing this stuff a long time. The product in the OP, as pictured, is a potential electrocution risk IF power shorts to the case from the PCB, compromised insulation, etc.
This can be fixed very easily by disassembling the product, drilling and tapping a small hole in the case, screw a closed spade lug to the case internally, run the wire over to the the plug connections (second picture in the OP) and solder to the ground lug.
As I say, it's easy, but if you screw it up, you can also electrocute yourself. Mistakenly solder to the hot, and you've energized the case when you plug it in.
Regardless, this product, as pictured, has the grounding problem.