The three prongs on a North American power plug are hot, neutral and ground. The ground is the round center plug and is tied, back at your circuit breaker box, to the same incoming wire as the neutral wire.
The neutral wire carries current back from the load (in this case, your MES smoker) and so, when things are working right, it carries the exact same current as the hot wire. The ground wire should carry no current and is there to provide an extra measure of safety, but only for those appliances that use it (many do not). When it was first added to electrical installations, back in the 1960s, appliance makers would tie it to the metal chassis or cage containing the appliance, and if the insulation inside that cage ever broke down and caused a short, the current would flow back through the ground wire, rather than through you (if you happened to be touching the appliance).
I have never been clear as to whether this actually improved safety much because it takes so little current to kill you. You will notice that many devices still use just two-pronged plugs.
The GFI was introduced a decade later in order to provide a LOT more safety, especially in damp locations, such as outdoors, your kitchen, and your bathroom. In those cases, you can be standing on a damp floor in your bare feet, and any electricity that manages to get to the surface of an appliance will flow through your body down to your feet because the ground has the same electrical potential as the neutral and ground wires on your plug, and the electricity is just as happy taking that path as it is going back through the wires.
The GFI measures the current coming in from the hot wire and the current flowing back out through the neutral wire. In normal operation, they should be the same. If the return current is less, that is happening because some of the current has found another path to ground.
In the case of the MES, it is my belief, from reading a lot of posts about this problem, that the GFI gets tripped either from moisture that has gotten into one of the two electrical boxes (most likely the one on the bottom), or there is some insulation that has broken down, probably around the heating element. Because the whole box is sheet metal (covered with vinyl on the outside), there are lots of places that might conduct electricity, if there is a problem.
Therefore, you might very well have an electrical hazard.
If you know how to use a multi-meter, there are tests you can take to determine if you have a problem. However, if you don't already know how to do this, I don't think I should describe it, because there are some hazards involved.
GFI plugs DO go bad: I've had to replace almost half a dozen over the past thirty years. When they go bad, they will trip even though there is not a problem.
To determine if you have a bad GFI, all you have to do is find another GFI-equipped plug and plug your MES into that. Since you won't be running it for more than five seconds, you can even use a GFI inside your house. If it trips several of them, then you do indeed have a ground fault in your MES, and you need to fix the problem. I would perform the test on as many GFI outlets as you can find, at least 3-4. If it trips them all, then you know, with certainty, that your MES is defective. Because it is a safety hazard,
Masterbuilt should replace the unit, because otherwise they will have liability. I would call them, tell them how you have tested it, and make sure to mention the word "liability."
If you want to first try fixing it yourself, my main suspicion is moisture. I suspect that moisture runs down the cord and into the hole in the back, and you should start with that assumption and see if you can tip the MES so that water can drain out. You can take further steps to try to dry out any box that you think might have received water from that power cord opening.