Tabby is a color pattern. It's like you can have a quarter horse that's a palomino, or a bay or what have you, but it's still a quarter horse. Or a Labrador Retriever can be black, chocolate, or yellow, but they're all Labrador Retrievers. Technically your boy is a red mackeral tabby with white DSH (Domestic Short Hair=mixed breed/alley cat/moggie, etc.)
You can really only be certain of breeding, or lack of same, if you know who the parents are without a doubt, and if the parents' pedigrees are recorded with a reputable registry.
Oh, by the way, I'm assuming he's a mackeral tabby, and not a classic tabby. Mackeral tabbies are the "tiger" stripe variety, and classics are the "swirly" or "bullseye" stripe variety. Hard to tell from his comfy position