Mickey Rourke did not receive an Oscar nomination for portraying Henry Chinaski in Barfly.
Mickey Rourke plays Henry Chinaski a character who does not see to give a damn about most things and plays the part as if he doesn't give a damn what anyone things either. Rourke goes for broke with his performance playing the role of his own very particular characterization and going all the way with it. Rourke goes all the way with every respect from the way he stands, the way he sits, the way he smiles, and especially his voice. Everything that Rourke does is not at all compromised in his seemingly rather odd way of playing Henry that pretty much its a love it or leave it type of performance.
I would say more then anything it takes a bit of time to get use to his performance as Henry as it is so strange on the level of conception. To Rourke's credit he does succeed in the way a performance like this needs to succeed in that he does make all the mannerisms and his voice seem natural to his character. Rourke is consistent though throughout in terms of his creation of Henry. He never falls off from this characterization and he always is the odd sort that Henry is no matter what the situation. Rourke never loses his character and although Henry always seems less then normal Rourke is always true to who Henry is.
As film alcoholics go this is a very different vision then usually seen. They are usually either comedic drunks or pained individuals who are slowly destroying themselves with their drinking. Henry as a character sort of doesn't fall into either category and he sort of falls into both. The tone of Barfly is quite unusual and this largely due to the way the character of Henry is written and the way he is portrayed by Rourke. Henry is a barfly in that he is always of that world and never stops being part of it which means he is always drunk in some way, but it does not seem self destructive, in the traditional way, as he seems to be exactly where he wants to be.
Henry just kind of does what he does throughout the film and the ending is of the film is that he is left as a man just continuing to do what he does finding that is all that he wants. What Rourke does quite effectively though is make Henry a man who would start at the bar and stay at the bar no matter what. He develops the oddly carefree personality that goes with the flow whether it is downing yet another glass of liquor, spending time with a fellow lush (Faye Dunaway), or getting in a bar fight he pretty much takes in his own way always without very few examples of really ever even getting bent out of his already rather odd shape.
Henry's lack of much of a character arc though is not a problem because Rourke does realize Henry so well that his lack of change is actually just what makes the most sense for his character. In turn the appeal of this performance is just Rourke having Henry be himself. Rourke's performance did take some time to get used to but once I did I found him quite a compelling character to follow. This character is all about the creation of Henry which Rourke just goes all the way with and it really does work in making the film itself work by making the titular Barfly a strangely interesting and sometimes even humorous character to follow.