"Play" is different to "games".
There are plenty of definitional debates in this area - where does 'theatre' end and 'games' begin? how exactly do 'sports' fit into this? - with little to be gained by trying to draw a precise line. But this particular distinction is useful.
"Play" is unstructured activity. It's imaginative and improvised and doesn't have clear win conditions. It's "I'm a fire engine" or action figures in the sandpit or calvinball. It might have a faciliator to get it started, but it never has designers or empowered crew roles.
"Games" have rules, winners, and losers. There might not be an alternate world at all, like soccer, or there might be one with clear roles, like 2.8 Hours Later. Any imagination players bring to the world must fit inside the provided structure.
You can do a game wrong. You can't play wrong. (Yes, the reuse of the English verb "to play" for games makes things hard, here. German apparently lacks even a noun for "play", so the distinction is even more difficult there).
Drawing this distinction helped me to realise that, by adulthood, most people have largely lost the ability to play - including me. We don't feel like we have permission, we're afraid of looking stupid, or we feel like we're wasting time. You can get better at almost any game, but you can't get better at playing.
There are people and organisations who are tackling this head on, trying encourage adults to play directly. I'm not one of them. Fire Hazard takes a subtler route. We make games that provide structure and permission to be someone else, somewhere else - to restart stalled imaginations and play without realising it. In the same way that Citydash turns non-runners into runners, all of our games should turn non-players into players.
And just as with the running, if they keep that going after the game, so much the better.