Why is there a grounding clip on this solder sucker instead of a third prong on the plug?
Some of reasons I can think of:

Some US plugs are still the original non-grounded outlets.

You don't necessarily want to ground directly to &quot;earth&quot;. For example, you may an inline 1MOhm resistor to protect the user from electrocution (e.g. touching mains).
If you were using the earth terminal on the plug, you would not put a 1M resistor for avoiding confusion as to the purpose of the terminal - safety connection vs ESD protection connection.

You may not want to connect to mains earth at all. All you need is an equipotential working area - and that equipotential level doesn't necessarily need to be mains earth.
You could for example simply connect yourself (via wristband) and the solder sucker to an ESD mat. This would ensure you, your workspace, and your tool are at the same voltage as whatever device is in the workspace.