The index value itself doesn't change on account of the split (that would be ridiculous). Visa's weight will drop, and every other stock in the index will increase accordingly. They use an index divisor to maintain the current level of the index when corporate actions like this occur: http://www.investopedia.com/terms/i/indexdivisor.asp
At this point, the Dow is only cited because "it's been around forever." That, and Dow Jones is owned by News Corp. So of course the media wants to keep promoting its own subsidiary.