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I think you are misreading the statute. The way I see it is:

The definition of the chemical dispensing device is " "Chemical dispensing device" means a device that is designed, made, or adapted for the purpose of dispensing a substance capable of causing an adverse psychological or physiological effect on a human being."

The exception is for " other than a small chemical dispenser sold commercially for personal protection" The exception is not a limitation on what threat you are protecting yourself from, but rather the size and source of the personal protection device.

Bear spray and dog spray would both would fall under the definition of a "chemical dispensing device" since they are capable of causing an adverse psychological or physiological effect on a human being, but if they are a small chemical dispenser sold commercially for personal protection (from whatever type of threat) then they fall under the exemption clause in the statute.