Thoughts

I took it as simply being his (and his particular branch of Christianity's) take on the Sabbath. Also, the story takes place nearly a century ago, when social mores across the board were more formal for everyone. Note that Eric Liddell doesn't yell & belittle & browbeat the boys playing football. He just offers a kindly reminder of what the day is supposed to be about for all of them. And does so with a fond smile, not a scowl. Perhaps remembering that he might have done the same at their age?

The belief in those days was that nobody should work on the Sabbath (except whoever did the cooking), and nobody should have fun either. Every memoir of a person who grew up in a Christian household in the early 20th century mentioned the dreariness of Sundays, when the kids were forbidden to do anything useful, and forbidden to play games. They were expected to read religious works and pray, and were forbidden to do anything else.

Of course the Sabbath rules forbidding work were bent when it came to the convenience of the Good Christians who forbad children from playing games, "good" Christian householders expected a good solid hot Sunday lunch and expected their wives and/or servants to work hard on the Sabbath to provide it. At least Judaism is better about that, there's a body of traditional recipes that can be prepared before the Sabbath and served without any work, plus they had the institution of the "Shabbat Goy", where a non-Jew is paid a few bucks to do things like light fires or fry eggs for breakfast.