I installed the wine package but it didn't work:
apk update && apk add wine && wine /bin/sh: wine: not found
Installing wine is fine your computer will now interpret .exe files. You still need a frontend GUI like PlayonLinux in order to actualy do much of anything as far as installing games and the like. If no package is available you will need to install from source. You will need build essentials and some other libraries to make and install the source. The info required to do this will be in the readme in the folder created after extracting.
Did you try running
On my environment I've done:
apk update && apk add wine && ln -s /usr/bin/wine64 /usr/bin/wine