Your animations are really smooth and flow pretty nicely, but the actual movement isn't necessarily as realistic as it could be. When a four legged animal runs, the back feet hit the ground first, not the front feet. You should try animating that kind of movement and see how it feels.
That diagram is pretty accurate, but it starts off at a weird place in the cycle. At the end, you can kind of see how the front leg is coming down just as the back leg is lifting up, although if you look at slow motion videos of dogs or horses running, you can see a little more clearly that the front legs usually touch the ground before the back legs lift up again. This is because the back legs (at least in horses) tend to do most of the pushing and the front legs are a secondary support to keep the body level until the animal's feet touch the ground again.
It's definitely harder to see in dogs because they do commonly lift all feet off the ground at once when they go fast enough, especially in a lighter weight dog with longer or more powerful legs. In that case, they don't need to bring the front legs down quite as soon to level out their bodies. It's mostly just about knowing where the pushing force is coming from and how much pushing force there is, and that all depends on the exact type of animal you're trying to animate. Like I said, it's usually much easier to see that kind of thing in horses because their bodies are so heavy and need more push and support to run.