How did evolution support sports, fun, entertainment etc
This answer can be from many different perspectives! I'll try to blend them all together as much as possible.

First of all evolution did not choose to make us love sports. Evolution made us social animals. And sports is just one of the tools we use for that purpose. Think about it, because if evolution gave us sports, then you will play sports, your kids will inherit that bit of experience from you and they would be that much better than you. But no, we all start from level 0 when we try to play any games or sports. This is because, sports is primarily a motor memory

So why are we social?

This study back in 2014 was one of the first to suggest that memory can be heritable. It generated a lot of attention and the authors themselves suggested that their findings were standing on a very capricious footing and required further validation. 

This point is valid because evolutionary forces require mechanisms by which features/mechanism which bestow advantages towards the survival of the species are positively reinforced. In this case social behaviour is the function. 

Do not go googling the word Social behaviour, for some reason the wiki article looks only at dogs and cats. That is unpragmatic, because we also have the same function.

I will broadly breakdown social behaviour into


Accommodation of non-aggressive behaviour from individuals in neutral territory.
A means to communicate


But, you may ask how does social behaviour benefit you? Well the answer is simple, increased survival capacity, and better chances of propagation.

Such studies exist in crows, which have studied social behaviour. Indeed, if you start to consider studies in behavioural biology, you would find that there are instances where female mosquitoes do not just mate with any male mosquitoes, even in this case you can call it a very rudimentary form of socialising.

So in your case sports is a tool which allows us to accommodate and communicate with others in neutral territory.

You can take a look at this which better explains the social aspects of sports