I think we have to understand the words of Swamiji with reference to the famous saying
śarīramādyaṃ khalu dharmasādhanam
This body is surely the foremost instrument of doing [good] deeds
Even with a common sense, we can understand that without a body nobody can achieve anything, i.e. studying Gita, Upanishads, etc, pondering over whatever that was studied and finally practicing whatever studied.
Everyone in general, who is in his teens or even in early 30s of his age, will enjoy a fairly good health (I am not quoting exceptions here). During that age, it does not matter much whether one does exercise to keep himself fit or not. The body can sustain prolonged study and hard work.
However, in late 30s and even further, the effect of non-doing of exercise will tell upon one's prolonged study and hard work. One will not be able to sustain for that type of hard work after 40's.
So in order to have a healthy body at old age for all persons in general and even at young age in respect of ill-health bodies, Swamiji adviced exercise.
As playing Football assures building up of strong body, which will sustain the prolonged study and hard work in spirituality