I have creases or small tears running throughout the perimeter of my tires.
Does this warrant replacing the tire completely?
I have only seen wear like that in tires that are around 10 years old. What does the date code say? Have you ever let a rubber-band sit for years? You are risking tread separation by driving them like this. If you can afford the tires you should replace them. An accident at high speed will cost you more than the tires.
Short answer, yes.
Judging by the date of manufacture, (0811) those tires are over 4 years old.
This alone is reason enough to not use the tires as the rubber will harden over time, even if it hasn't been used, let alone with peripheral cracks like the ones shown!
I had a almost complete tread separation on a 6 year old tire on the front while driving on the freeway. Luckily I heard it start thumping and was able to get off the road right away. The other front tire was about to start doing the same thing. I replaced all 4 since they were about the same age.
I now believe it's a good idea to replace the tires after about 5 years no matter what the mileage to be safe, but that's a personal opinion. Reading the manufacture date code on the sidewalls is easy.