The fact that someone would ask implies that the title does not make it obvious.

The time to factor one giant number is interesting, but so too is how this method applies to other, especially more common, problems.

RSA with keys less than 1024 bits long is not considered to be secure against classical attack, so SSL/HTTPS is presumably not using such key lengths. The construction in the paper still takes hours on 1024 bits, therefore it will not break SSL/HTTPS in minutes.

If you were to, very inadvisably, use RSA with 128 bit long keys (maybe that's what they were asking?) then yes it would take minutes. But you can already break such keys in minutes using classical computers.