Translation:His problem is drinking too much alcohol.
There's something about this that seems odd to me. "His problem is drinking too much alcohol" seems a bit like the problem drinks alcohol. Maybe "His problem is that he drinks too much alcohol." would be better. I could be nit-picking here, but it just seems odd. :p
The problem only exists in the English sentence — that's the nifty thing about these verbal nouns, is that it's a noun where in English we would often use an infinitive verb. It helps to clarify issues exactly like this one :) (I agree, the English sounds a little funny!)
Seems like the problem is that in English, the present continuous is the same form as the gerund. The upside is that it can make for some interesting word play :)
I'd say it sounds awkward in Polish as well. "Jego problem to picie." is what a Pole would say. It's so obvious that it's too much of alcohol that it's not even mentioned.
Thats because mentally "drinking" = "alcohol" :) "On ma problem z piciem." - He has the drinking problem. And the oposite but also popular statements would be: "Jego problem to alkohol." or "On ma problem z alkoholem." I would say that this sentence is less awkward if you say: Jego problem to picie zbyt mało alkoholu [too little of alcohol]. e.g. He drinks too litle so it is not in the righ mood :). And the information doesn't look duplicated any more.
I tried to convey the thought of alcohol being massively consumed by OTHERS :-)
But missing "z" sounds as if he used other people... as straws ;) Or something like that. Using them as an 'instrument'.