Of course, it matters what the baseline frequencies of these cancers are. If these represent .1% of all cancers, even a tenfold relative risk only increases your absolute risk by 1%. That would be "significant" under some definition of the word significant. But it might not be decisive for someone considering whether they should drink.

On the other hand, if the baseline rate of those cancers is 8%, it would likely be enough to convince everyone to stop drinking.