Apple ID from other country no longer works

You can log into an account even if the email address no longer exists as long as you don't end up doing something that requires you to respond to an email being sent to that address. You can also simply change the email address on the account. Here's how you change the email address you use for your Apple ID:

1. Go to https://appleid.apple.com and sign in.

2. In the Sign-In and Security section, choose Apple ID.

3. Enter the email address that you want to use as your Apple ID.

4. Choose Change Apple ID.

5. If you changed your Apple ID to a third-party email address, check your email for a verification code, then enter the code. Learn what to do if you didn't get the email. --> If you didn't receive your verification or reset email - Apple Support

6. If you use services like iCloud or Messages to share with friends and colleagues, sign in to those services with your updated Apple ID. --> What to do after you change your Apple ID or password - Apple Support

For more details see the document Change your Apple ID - Change your Apple ID - Apple Support

Unfortunately you did not do that when the old email account was active so if the above method does not work, you may have to contact Apple:

Contact Apple for help with Apple ID account security - Apple Support

Note that you can only update Japan specific apps by being logged into the Japanese version of the App Store. To do that you must have an account set to that country. The way you were doing it before, while possible, is not the way the system is designed* (plus you have to keep settings up to date on both accounts). Instead you would change the country settings on a single account: Change your Apple ID country or region - Apple Support

I too have lived in different countries and when you move you sometimes have to say goodbye to some things and embrace new ones.

*Apple Media Services Terms and Conditions -

Legal - Apple Media Services - Apple

"Our Services are available for your use in your country of residence (“Home Country”).

Unless the game also exists in the US store then you will need to be logged into the Japanese store in order to update it.