Eh. If you're not family, you can miss alcoholism fairly easily. Whether Nolan is overdramatic is of course a different question.
Another factor is that alcoholism needn't be a case of drinking all the time. It can happen only occasionally, but instead of drinking at a party, it's depressed drinking, together with watching the old film's of one's youth, reminiscing about a time long since passed, while the person doing the drinking is himself not quite there anymore, yet the aura, if you will, of them getting lost in the alcohol is all over the house and drags everything and everyone down. The family can tell what's going on and that the person they remember isn't there anymore, replaced with an intoxicated shadow of his former self.
And then, of course, the littlest thing can set that person off.