I have no experience with the Ithaca Deer slayer. However, I make muzzleloading rifles to earn most of my living, and I can tell you that a good muzzleloader with a good barrel is EASILY capable of killing deer at 200 yards. So if the ammo was up to the task, and if the barrel is of high quality I would not disbelieve their statement.
You see, most bolt action rifles you can buy today are capable of hitting the vitals of a deer at probably 800 yards, but one in 5000 men is capable of that.
Long shots with muzzleloaders are very easy IF and only IF you know the load, and are capable of judging range.
One time against a bet I hit a yellow quart Pennzoil bottle at 250 yards with my flintlock 62 cal rifle 3 times out of 5 shots. I won the dinner. The man I was betting against told me I could not hit it at all.
Now, I shoot that rifle a lot, and I know how to hold the sights out to about 275, so I was confident that I could make those hits I missed 2 times, but I was close enough to make the bottle bounce. Obviously ALL those balls would have killed a deer.
So if the Ithaca is as accurate as my flintlock (which I’d bet it is) I can believe their claim with no problem.