My grill is on concrete squares with crushed stone, so I don’t use any fire extinguishers outside. That said, you can’t be too safe and it’s nice you’re thinking of it.
My first thought is that it’s smart it’s a chemical extinguisher that will stop grease fire, but my second thought is the can might be too small for a grill situation (looks like it’s a pan size). Additionally if you did have to use it, I’m not sure what chemicals are in it, something like baking soda would do the same job as the can, but still be food safe.