The Play Store does not work in isolation. It requires to function. If you install the Play Store but don't have the correct Play Services for Android 4.4.2, the store will open, but you won't be able to download apps or it will crash immediately.
When searching on mirror sites like APKMirror , look for versions specifically tagged for . play store apk mirror android 4.4 2
For KitKat users, the "frozen" state of the OS means you must look for the to keep your apps running. Recommended Play Store APK Versions for KitKat The Play Store does not work in isolation