Russia is the clear winner with 70 points, while Canada's 55 points edges out Norway and the United States who are tied third with 53. The overall rankings are only tweaked a little, which is good not to upset the apple cart entirely. One modification I could suggest is to count team sports for more points since it's impossible for a given country to sweep the medals (i.e. Canada's men's hockey team can win at most one gold while the Netherlands can, and have, won multiple medals per event). Then again sweeping the podium is an equal opportunity event hence I'm not going to change the table.
I forgot to mention a third way people rank the olympics, which is dividing that countries' population by the metal count to 'normalize' the rankings. You could do that here too, but with points instead of using the (oversimplified) medal count. Here's the rankings again with a points per capita: