When it comes to how an athlete's legacy is judged, the degree to which championship wins are factored in varies widely by sport. In baseball, being a no-ring stat god alone, e.g., Ted Williams, is usually more than enough to be considered an all time great. Not so in basketball or football; especially if you're a quarterback. When it comes to quarterbacks, Shannon Sharpe will tell you: "You don't even get to get in this discussion if you don't have a championship."
Dan Marino, who once held nearly ever passing record, "never won a Super Bowl," and this is mentioned frequently as a serious mark against him. Meanwhile Joe Namath, a pretty mediocre quarterback, is a legend only thanks to a Super Bowl victory.
In football, this YOU AREN'T GREAT WITHOUT A RING criterion is especially goofy. No sport, not even baseball, has as much specialization as football. In basketball, the players play both defense and offense. Same with baseball; you field and hit (unless you're a DH/AL pitcher). In football however, you are literally one or the other. Eleven entirely different men get on the field when it is time to play defense. Dan Marino was never responsible for a single defensive play; in other words, he didn't participate in 50% of the game, but somehow he will never live down not winning a Super Bowl while playing on just one side of the ball. The very fact that Marino could break that many records and still not win a Super Bowl shows how impossible it is to do it alone. Given how many moving parts there are in every single football play - defense or offense - effectively pinning it all on one player seems a bit absurd.
Maybe in the days when football players played on both sides of the ball this criticism was more valid. But pretty much no one has done that since 1962. It might be time to move on.
This whole line of thinking can be smashed quite easily: tomorrow you're starting your own football franchise with your own dough on the line. Who you do want at quarterback: Dan Marino, or Jim Plunkett? Don't give yourself a hernia trying to remember who Jim Plunkett even was...
As for why basketball greats like Karl Malone and Charles Barkley get more abuse for not winning the big one than Ted Williams or Ken Griffey Jr., well, I think part of it is simply that basketball is now a much more beloved/discussed sport than baseball, mainly because of a guy named Jordan. And when people think Jordan, they think championships; six, in fact. His Airness remade the game, and others' judgments of the game, in his image.