Hmmmm... Mom, Dad and 10 year old brother. This sounds like a perfect situation for a two year old to be getting his needs met too quickly so that he has no need to talk. You may want to do an evaluation of how you are meeting his needs and see if you aren't all overanticipating and meeting his needs without him having to learn to ask.
You also mentioned him watching reading videos. That's ok, but are you sitting down and reading children's books with him? That's one of the best ways to help a toddler begin to develop vocabulary. Don't just read the pages of the book, but pause and give him time to point out things and give him the words for those things pictured and encourage him to try to say the words.
Take walks with him and point out different things you see on the way. Hold a conversation with him, as you go, and give him time to respond to what you say. Sometimes we tend to just keep talking so much that we don't give the kids a chance. When you are out in the car going places, also keep up a conversation with him. Point out things.. stop signs, various vehicles, people, buildings, animals... whatever you can see that's interesting. We have a 2 1/2 year old in our daycare who will point out busses, and tell us what kind of bus it is. He had a real argument with the 3 year old one day because the 3 year old wants to call all busses "school bus" and the younger boy has been taught by his mother the difference between a school bus and a city bus. I don't know a kid who doesn't love trains and airplanes. When you see one, talk about it. Not just "there's a train" or "there's a train" but talk about how big it is, how close it is, where it might be going. For a train, you can count how many cars it has, maybe what colors the cars are, the type of cars if it's a freight train. Point out various things like the wheels and how they go... the possibilities are almost endless.
I have said this before and will keep saying it, we adults often have a tendency to talk down to children or talk over their heads, when what we really need to do is talk with our children, treating them like real people. This means no baby talk ... or at least strictly limit baby talk. When he begins to use words and has his own way of saying them, enjoy the unique ways he says the words, but repeat the words correctly back to him... not as if you are correcting him, but just naturally in your conversation. I like to write down the ways our kids start saying words and even write them again as they begin to say them more correctly. These are special memories to save for the future, but our job now is to help them learn and grow, not to repeat back their mispronounced words to them so that they are reinforced.
I doubt that your son has a problem that will need therapy. If he does, then by all means get the help as soon as his Dr. deems it necessary. But, I do really think that you can have him talking before long. Your next post may well be "how do we get this kid to quit talking so much?"