TLDR- Go offline and try to play the game. If this doesn't work and you get some kind of message about having to be online, you have to update the game.
The only way I could think to do this is by turning on airplane mode or essentially going offline and then launching the app. If there is any offline portion of the game it may let you play, although most apps require you to be online now.
If there is no single player aspect of the game, you will have to suck it up and update the app. Even if there is, you may have to update anyways.
The main reasons they force you to update apps are the following:
- Balance: Any game with online/multiplayer needs to be balanced and all players need to play on the same patch. With this point, you may be able to get around it by playing offline but more recently, you may not be able to due to the following points.
- New features/characters: Any new features or characters need to be added to keep users coming back and these need to be added to a variety of places, one of which being the code. The only way to get that new content to users is with patches and since mobile games are a treasure trove of microtransactions, most companies want to force you to see that cool new character or shiny new outfit you need to spend money on to realistically get.
- Bug/exploit fixes: The main reason that single player mobile games have started to require an internet connection is to ensure users are not running old versions to exploit some old bugs. Since most of these exploits allow the player to avoid spending real life money on the game, it is in the developer's best interest to patch those exploits.
As a disclaimer, I haven't played the game but this is the general trend that mobile games tend to follow.