It's an adjective, meaning someone who plays sport with the highest possible principles, way exceeding normal sportsmanship. I'm not sure which is the chicken and which is the egg, but there's a link one way or the other with w:Corinthian F.C. - see the talk page there. --Dweller 12:52, 10 December 2008 (UTC)
Senses I've found in glossaries are not quite so positive:
An early usage: Corinthian Tom and Jerry Hawthorn in Pierce Egan's Life in London (1821). I don't know which sense if any would connect to this usage and what the realtionship is to the football club. DCDuring TALK 00:06, 14 December 2008 (UTC)
A religious work of 1807 may convey the source of the "rake" sense: Paul's Epistles:
Reputedly corinth had some thousand harlots at the temple of Aphrodite. To "act the corinthian" meant to be a harlot, in Aristophanes. They also hosted the w:Isthmian games, one of the three or four major sporting events that occurred every four years (like the Olympics) in Greece. Plenty of ambiguity. The name would have provided cover for the minister and the family, while hinting at more. DCDuring TALK 00:43, 14 December 2008 (UTC)
It's probably an exclusively British (or perhaps Commonwealth) usage, but I found plenty when I googled "Corinthian spirit" in uk sites. This was one of the clearest, being not just a usage, but offering a definition too. --Dweller 10:55, 15 December 2008 (UTC)
Corinthian spirit seems to warrant a wiktionary entry, where "Corinthian" alone does not often seem to carry the sense, though it might warrant a sense. google books finds book titles containing "Corinthian spirit". DCDuring TALK 12:25, 15 December 2008 (UTC)
As an example of current usage, see this article in a U.S.-based sailing magazine in which the implication seems pretty clearly to be a dedicated and well-invested, but distinctly non-professional, weeknight-and-weekend amature sailor, certainly with no negative implications:
In this context, "Corinthian" raceboats would be like a road-going sports cars in contrast to a Formula racer or other track car.