Install it, open H2H, and sign in with your usual e-mail and password.
Not sure yet? See how it works →
That older copy came from a download, not from Google Play, and the two can't update each other. Uninstall it once (hold its icon → Uninstall), then install from Google Play above and sign in again. Only the sign-in is lost — your matches, picks and scores are on the server.
You're all set. Updates arrive on their own through the Play Store — you never need this page again.