He looks like a nice horse but I have to agree with Palomine, he's not a WP horse in any shape or form.
If you enter in small shows, he might do well or he might not...it will all depend on who else is in the class.
What I'm about to write, I don't want you to take personally because I'm not being derogatory toward your horse, just pointing out what I see as comparison to an ideal WP horse.
Your guy does have too much action in his legs which is creating the bouncy trot, WP horses have almost no bend in the hock or knee while they are moving. Also, just judging on this video, which is old, he's not even remotely collected. You've got the start of a headset (though, like Greentree, I see more of a dressage headset than a WP headset...too much arch in the neck and his chin is too tucked, looks to me like he's evading the bit), but his hind end is hanging way out behind him and isn't engaged at all. Add into that that he's got a naturally higher headset due to his coformation and you're going to have twice the trouble getting a flat topline from him.
By all means, keep working on his training as being trained to collect and slow his gaits will make him an all-around better horse, show the heck out of him in whatever classes you want, but don't get upset if he doesn't place in the pleasure classes.
He's just not designed for it, simple as that, but that doesn't mean that you can't enjoy them