^ Couldn't get the provided link to work. I modified your link and used this one:
www.youtube.com/watch?v=JhYEWDZbQX0
The step shown is not really a pitcher's stride (which I has assumed is what you were trying to implement since you indicated that you are/were a pitcher). A step of that magnitude should not be a problem not a foot fault), but I don't think that it is really necessary.
In one way, the tennis serve might be a bit more like throwing a long ball in from the outfield. Instead of throwing on something close to a horizontal plane, the serving motion is more like throwing at a steeper angle -- perhaps something like at 45 to 60 degree angle upward.
Actually, the first part of the service "throwing" motion is even steeper than that. In order to achieve a decent
racquet drop (which facilitates hitting "up" on the ball), the throwing angle is nearly vertically upward -- you would be throwing at an angle that is more like 75 to 90 degrees upward. The throwing motion used for a tennis serve is something of a blend of these 2 throwing angles -- the 1st part is nearly vertical, while the throwing action just prior to contact and just after contact is more like the 45 degree throw.
Not that the knees are bent and the legs drive upward on the serve. This also facilitates hitting up on the ball. The legs are used in somewhat of a different manner when throwing a baseball. Try to get your hand on some old, cheap or broken tennis racquets. Take these out to the park and trying throwing these instead of throwing balls to simulate a serve. First, try some throws at the 45 degree angle. Then, to work on a deep racquet drop, perform some 75+ degree throws.
In you are interested, I can talk more about pronation (forearm rotation), the role of the tossing arm (after the ball release), and the action of the back leg. I suspect that all of these will differ from your baseball throw.