No … this is not a parody. It’s real, and it’s been available since October from the Texas-based Exceptional Products. (Here is its entry over at Snopes.com.)
It STILL feels like an intentionally satirical product … the ad is just too over the top. (The James Earl Jones soundalike and the golfing stuff seem like obvious jokes.) Is it part of the parody that the bear also is the national emblem of Russia? (Yes, I know teddy bears originate with Teddy Roosevelt, but still.)
Trumpy Bear arguably brilliant, too. Think about it … this thing is going to sell. And yet it also appears to caricaturize the very same people that are its target demographic. (Many will buy it without realizing it is a joke at their expense.) Which makes it a damned clever act of trolling.