Is he committing a crime in Albania?
It would help if you posted the statutes that regulate or prohibit betting, since the terms thereof would shed light on the legal definition (aka prima facie elements) of betting and/or the legislative intent behind those statutes. Absent that information, your description reflects that most certainly the Albanian is committing a crime.
The Albanian's conduct matches --at least-- the ordinary meaning of betting: he is not disbursing (or promising to disburse) money merely for fun or leisure, but for the prospect of possibly profiting from an uncertain event of which he officially has no control. Doing it through a third party located in another country changes nothing in this regard.
Am I committing a crime in Italy?
The Italian might be considered an accessory of that conduct being classified as criminal in Albania. Thus, facilitating activity that is prohibited in Albania could turn out to be problematic even for the Italian.
Furthermore, even if betting is legal in Italy, the Italian might be in trouble under the laws of Italy if taking money (without the requisite license) from someone else to make bets constitutes unauthorized business of gambling. The condition that the Italian would retain a portion of any profits makes the business (or for-profit) element quite evident.