If you’ve ever “been there”, some songs truly need no explanation. IMO these are two such songs.
If you’ve never “been there” with respect to the first song, consider yourself a truly lucky individual.
If you can’t identify with the latter tune in some way . . . you have my sympathy.
Author’s Note: yes, the article’s title is correct. Sting’s given name is “Gordon Matthew Thomas Sumner”.

Always thought the first one a bit creepy – kinda like a stalkers anthem. Never able to turn that into a positive, although it can be done, surely.
The second is even more poignant now than it used to be.
Here’s a creepy one from Phil Collins:
https://www.youtube.com/watch?v=Itxh1ALqJFs
Phil Collins has no end of creepy/stalky songs…Misunderstanding, Don’t Lose My Number, Just a Job To Do, Something Happened on the Way to Heaven, and definitely the one you reference – lots of stalking, hunting folks down, you can’t run from me shit…
(I still love the guy…)
Sting is one of those artists who I liked when he was in a group, but like better still as a solo artist.
Throw in a few more, like, “Shape of My Heart”, “Fragile”, and, “Desert Rose” in there too.
https://youtu.be/Zn7eWTsj9wU
Don McLean … Vincent
https://www.youtube.com/watch?v=oxHnRfhDmrk&index=29&list=WL
Meat Loaf … Rock ‘n Roll Dreams Come True
https://www.youtube.com/watch?v=j7-i43W4mqw&index=43&list=WL
First one also AKA “The Paranoia Song”.
Had a part-time job in a jewelry store when I was in school. A young lady bought a pocket watch as a wedding gift for her fiancé. To make it extra special, she wanted the inside case engraved with “Every breath you take, every move you make, I’ll be watching you.” I remember, right before writing up the special order, looking at her and asking “Really?” She was a serious as she could be.