There is a class of workers that provides necessary social services - "ox in the mire" kind of things - such as emergency health care and protection from evil-doers. Your doctors, soldiers, policemen, etc. fall into this category

On the other end of the spectrum, there is a class of workers that provides entertainment - certainly not a service that is essential on the Sabbath. Athletes, musicians, actors, etc. fall into this category.

Past prophets have been pretty bold in stating that watching or participating in sports on Sunday violates the commandment to keep the Sabbath holy (Spencer W Kimball and Joseph Fielding Smith gave several talks on this). Recently, General Authorities such as President Monson have given conference talks that praise athletes for refusing to play sports on Sunday. At least once a year, the New Era runs some sort of formulaic story about a youth on a highly-competitive travel team that missed a championship game on Sunday, but felt good for doing the right thing...

It's pretty obvious that the Church (and God, if you believe in the Bible and/or the Church) frowns upon Sunday play.

I have a hard time whenever anyone tries to use the "provide for family" defense to justify someone playing on Sunday. These guys have college degrees, and - in theory - are capable of providing for their dependents in a bunch of ways that don't require the perpetuation of Sunday sports (which the Church is against). Doesn't mean I think the pro athletes are bad guys for playing/practicing on Sundays (I don't). I do, however, think the decision to play on Sunday is a poor one.