Finnair isn't that large, really. Other Nordic countries, each one small, have SAS which is actually one of the largest in Europe, plus they have other domestic carriers. Switzerland is a small country but Swissair is a decent-sized airline. But true, Finnair has become very succesful for an airline originating from a small, remote corner of Europe. I guess they have done so by paying attention to quality. Finding a market niche (the Gateway concept; basically Helsinki as an East-West hub) has also helped a lot.
And actually, they _are_ competing hard with SAS, at least in Sweden. They have Arlanda as a sort of mini hub with direct daily flights to several major European cities. No such conquest to Norwegian or Danish heartland yet, but just you wait!
Now of course SAS took over Air Botnia, thus creating domestic competition for Finnair. But hey, that's only healthy!