Integer factorization is likely not an NP-complete problem at all. It is suspected (but not proven) not to be in the class of NP-complete problems. There is no reason to believe that an NP-complete problem solver can factorize integers in polynomial time.
Contrary to this machine it has been shown that quantum computers can solve the integer factorization problem in polynomial time through Shor's algorithm. But quantum computers are not known to be able to solve NP-complete problems in polynomial time.
Even quantum computers are far off factoring the RSA numbers because of the practicalities of the real world. The current world record Shor's algorithm computation is finding that 15 = 3 x 5.
You're misunderstanding the relationship between NP and NP-complete.
Integer factorization is in NP, which by definition means that anything that can solve NP-complete problems efficiently can also solve factorization. The question that's currently unresolved is whether factorization is easier than NP-complete, not harder.
I happen to have read the Wikipedia page on Shor's algorithm not an hour ago, and apparently they factored 143 without Shor two years ago. We're not quite there just yet, but 143 is getting a bit less laughable than 3x5.