Having an EE degree (although a LONG time ago), wa0auu's explanation is the correct one: the GFI looks at
current, not voltage, and compares the current going
into the smoker with the current coming back. The two must be equal. If they are not, some of that current found another place to go, like through your body and out through your bare feet standing on concrete. This can happen if there is moisture between the hot lead and something that eventually touches the floor, or if there is insulation breakdown, or if a wire has come loose.
The GFI is not a circuit breaker and is not necessarily going to trip if something shorts out or starts drawing too much current.
The idea of putting the smoker on a sheet of plastic or a dry cardboard box is a good one, and should help determine if there really is a fault to ground. Either of those items will completely insulate it from the floor.
In my experience, GFIs in outdoor receptacles can get very flaky and start tripping, sometimes with nothing connected at all. When this happens you have to replace the GFI. When you do replace them, get one that is labeled "weather resistant," or something similar. Here's one of hundreds of weather-resistant GFIs (I'm not necessarily recommending this particular unit):
Weather Resistant GFI
These weather resistant units have additional potting material around the electronics that makes them last a little longer in damp locations. Also, check the outlet's receptacle for signs of moisture. Just two months ago I had to replace the box next to my BBQ (and which I now use for my smoker) because the weather seals had failed and the inside was actually partially filled with rain water. Needless to say, the GFI failed.
Finally, just as a fun fact, I used my "Kill-A-Watt" power meter just now to measure the power consumption of my new 30" MES:
Plugged in, but controller off: 1.0 watt
Plugged in, controller on, but not heating: 1.5 watts
Heating (red light on): 777 watts
I'll try to remember, the next time I smoke, to leave the Kill-A-Watt attached the entire time. It has a neat feature that is useful for things which turn on and off while operating (like your fridge) where it will "accumulate" how much power is used during the entire measuring period. This should let me give you an idea of how much electricity is used for, say, a four-hour smoke. Of course ambient temperature will be important (it will require more power when the outside air temp is 30 degrees F then if it is 95 degrees), so I'll have to include that when I report my measurements.