No. You can just Google search the name of the game and download the .exe file of the Bingo Blitz game. Then, you can install it yourself. In this process, there is no need to sign in with your email account.
But if you want to download the Bingo Blitz game from the Microsoft store, you may need to sign in with your Microsoft account.
For the Android version of the Bingo Blitz game, you can download the game apk from Google and install it yourself too. But, in case you want to install the game from Google Play Store, you have to sign in with your Gmail account.