On allbreedpedigree you can make a pedigree for any type of horse, and make it any breed. Since there isn't a picture for the horse on that page, it could be any horse named Jack in the world.
Although that could just be a glitch on that page.
That whole geneology chart looks off. He can't be a Thoroughbred if his mom is a Quarter horse. End of story. He can be an Appendix QH, which is a first generation mix of a QH and a TB, but yeah....I generally don't like allbreed because I've seen them mess up tables before. I put my guy (a papered TB off the track) and it got some of his grandsires and such completely wrong.
That has to be a mistake. He can't be a TB... He's 3/4 QH and 1/4 Paint. If he isn't registered, I'd call him a Paint if he's spotted and a QH if he's solid.
I hate allbreedpedigree too. My mare is a purebred Missouri Fox Trotter... One of the horses about four generations back in her pedigree happens to have the same name as a Haflinger, and sometimes the Haflinger will randomly get put in her pedigree in place of the MFT of the same name. It also changes his parents and their parents and so on... so it looks like she's full of Haflinger blood, haha.
Technically, because of the Paint bloodlines, he's a Paint regardless of his color. He would only be registerable with the APHA, not the AQHA. My Paint mare has a very similar pedigree - two generations back, she's all racing QH and TB. Even if she was solid, she'd still be a Paint.