How about this recent Neil L Anderson talk that celebrates Sid Gelwix for refusing to play or practice professional, international rugby on Sunday?
https://www.lds.org/general-conference/2011/04/preparing-the-world-for-the-second-coming?lang=eng&media=video
How about this talk from President Monson, where he praises a Mormon that refused to play in a championship basketball game that was hosted on Sunday?
https://www.lds.org/general-conference/2010/10/the-three-rs-of-choice?lang=eng
Here is a page with some of the teachings of Spencer W Kimball - you'll notice that he talks about how some medical professionals must work on Sunday, and that he speaks negatively of "ball games" that are "played on the sacred day."
https://www.lds.org/manual/teachings-spencer-w-kimball/chapter-16?lang=eng
Then, of course, there's God... He said that "In it [the seventh day] thou shalt not do any work" Christ clarified that a bit, with His teaching on the "ox in the mire." (However, no one should deliberately put their ox in the mire each week, or let him get in the mire with no effort to keep him out -
https://www.lds.org/ensign/1978/01/the-sabbath-a-delight?lang=eng)
I could go on, but I think you get the point. There is definitely a consistent doctrine that is being taught...
And I'm not a fan of that "supporting family by playing professional sports" line. These guys have college degrees, right? They have name recognition as college stars, right? Is a career in professional sports their only viable option? Couldn't they adequately support their family doing something else for a living? I'm not saying they're bad guys for playing on Sunday - but I am saying that I think the decision to play on Sunday is a bad decision.