This only works on RSA keypairs (and any other cryptosystem that uses prime factoring) and it is inapplicable to the elliptic curve cryptography that Bitcoin uses.

Elliptic curves take their private key as an extremely large number and multiply that by a curve point to get the public key. It's completely different from getting two primes and multiplying together to derive the private key, public key and other parameters, which is what Shor's algorithm applies to.