If my stew beef is tough (it's been on a small flame in liquids for about an hour), does it mean that it is overcooked, or undercooked?
Generally speaking when speaking of "stew beef", the meat will break down more the longer you cook it. I often make shredded beef for tacos out of that cut by simmmering it for a few hours or more. At 1 hour, I'd say it was undercooked.
In there he recommends using stewing beef, browning it first and then "... stew until the meat is tender and can be cut with a spoon. This will take at least an hour and a half."
It sounds as if you have not rendered all of the fat properly. The fat needs to melt slowly and coat the protein molecules in the meat. The protein molecules will unwind (denature) during cooking, and then attach to each other (coagulate). The fat will coat them and keep them from clumping together in a tough bundle.
Your cooking technique of a slow simmer is correct, but this takes a long time. On high in a slow cooker or on a stove-top I'd say about 4 or 5 hours. On low in a slow cooker you need 8 to 10 hours.
In short, it's not about getting it done from a food safety perspective (although you should), it's about make sure all the tissues break down.