Oh dear. You seem to think that Bitcoin is some website where you stick your private key in and get authenticated as the "as the owner of that wallet".
Can you use the API key to control your funds without using the website that issued the key? Does the API key allow you to receive/spend funds offline (cold wallet)? Can you use the API key to sign a transaction and put it on a public ledger where anyone can verify it?
Just a few basic features of a Bitcoin private key off the top of my head. I'm sure you can find more on Wikipedia.