I've shot several running Coues deer and Javelina, and here is what I've found,
At 100 yards I lead it around 6 to 8" with my 7x08 and a little less with my 7mm Rem Mag, at 200 yards I lead it little over 2 feet. At 300 it's around 3 and a half feet. These are on an animal running full speed.
I've done tons of dove, quail and duck hunting in the past which helped tons on learning to shoot moving targets, also used to practice on moving silhouettes at 350 meters.
The 10' lead at an elk at 300 yds is way off, you'll hit the elk behind it.
Coyotes are great for practice on moving targets, they are fast and small, and fun to shoot. If you can hunt hogs in your area in open fields that's a another great way to practice on moving targets.
When shooting at moving targets there's what we call the "follow through" which means you keep swinguing the rifle/shotgun when you are pulling the trigger. Otherwise if you stop you fall behind and miss the target or end up with a gut shot or hit a hind leg.
Shot some skeet in my life. As I recall I was a fair 100/100 shooter, not so good at sporting clays. Always dropped a couple. Shot a lot of animals running too over 55 years of actual hunting and competitive shooting. (See)
So if we want to get into the weeds lets.
While I find 122" to be a lot of lead, it matches my experiences pretty closely. At 300 yards a bullet leaving the muzzle at 2900 fps has a time of flight of .35 seconds. An elk traveling at 20 mph right to left will cover 10.26666' in .35 seconds. If swinging the gun at the same speed as the elk was traveling worked as advertised a shooter should need virtually no lead at all. But then deceleration enters into the equation and lets not forget the lock time, the time it takes pressure to move the bullet, the .1-.2 of a second from the time the brain says fire to the time the finger pulls the trigger. All this means that two ppl shooting the same gun would probably need different leads to hit the same spot on a moving target.
Assuming a shooter can match the speed of an elk that runs at 25 mph and can run at 45 mph while his chest is rising and falling 20 to 30" inches a couple times a second and keep still the cross hair aimed ahead of him at a point in space, pull the trigger and not stop the gun, the lead theoretically is not 10 feet. It should be zero plus the deceleration of the projectile over distance/time converted into lead. The variable is a few inches. So still a theoretical zero lead.
I cannot imagine actually shooting off hand at any running animal much past 100 yards. Although I have. I use the swing thru method. But more often than not it has been at an animal that stopped for a millisecond.
The 10 foot lead is based on the ambush method which is often used for walking humans. I know at 12x my vertical hashes on the cross are x feet at 100-200-300 etc. As a rule I would not shoot at a running animals under any circumstances at 300 yards. But a walking animal would always be an ambush shot for me using my right left hash marks and always a center chest hold. The point of the ten feet is to demonstrate that at 300 yards from the time you pull the trigger, whether swinging or ambushing that animal will move 10' @ 20 mph. The ethical kill zone on an elk might be 14". If your swinging lead estimation is off just a few inches you will wound that animal.
Yes, we swing a shotgun, but unlike a rifle bullet, a shotgun gives us a shot string that may only be an inch or two long at 20 yards but gets longer and wider the farther out because different parts of the string decelerate and expand at different rates. So you may screw the pooch and still break the bird with the back or side of the string which now has length and width, both of which convert to an ever increasing likely hit window. Not so with A rifle bullet that is 1-1/4" long and .308 wide. So whether you use the Churchill method, swing thru, sustained lead or the Force, what works for a shotgun at 20 yards is not going to work for an elk at 300 off hand with a rifle.
The attached photo is of the entry point on a full 40-mph running red hartebeest at 123 yards. In the neck. He didn't bleed. Died so fast the blood looked like a red wax seal on a document. He was running away, not across but up and down a couple feet at a time. I fired the bullet at a spot about 4" above his head and he jumped right into to it. I ambushed him. The gun was not moving up and down but I will concede that years of upland, waterfowl and clays shooting didn't hurt.
If you or anyone can consistently make running shots you have a gift that is not teachable and also falls beyond the ability of 99% of people.