No. Encryption is just one type of cryptography, used to make data unreadable without the secret key. Signatures are something else, used to prove that the holder of a secret signed the public data. Zero knowledge proofs are another, used to prove you know a secret without revealing it. It's a fascinating subject.
I'm not saying all cryptography is encryption, I'm not even really talking about signatures, I'm specifically talking about asymmetric cryptography. I don't see any example of "asymmetric cryptography" which is not just a usage of public-private key encryption.
If you're talking specifically about RSA, then it's true that encryption and signatures both use the same type of asymmetric math, but in opposite directions. But most asymmetric cryptography doesn't have this property.
But the signature is an encrypted hash value, which is decrypted when verifying the signature. Maybe you could say signature verification as a concept is not encryption, but certainly Bitcoin's implementation uses encryption, and I don't think there's any definition of 'asymmetric cryptography' that is not also some form of encryption.
I'm not an expert on BTC, but I'd guess that if you can derive the private key of a signature from its public key (which is what the paper is describing), you can use that to place transactions from said wallet on the blockchain (ie. spend that wallet's money), right? Genuinely curious if I understand this correctly, there's a lot I don't know about how bitcoin's protocol works.