Sending, receiving, and organizing email in Outlook.com
When was the last time you signed into this "old" email?
If you haven't used this account during the last two years, it is unfortunately closed permanently and cannot be recovered. Microsoft's account activity policy is explained here: https://support.microsoft.com/topic/microsoft-account-activity-policy-7c0a9fa7-0982-b7c6-fd72-df852b63699f
In that case, you would have to work with each gaming service to see if they have a recovery process for this scenario.
For example, if you registered a Microsoft account or a Google account with a third party address, and you lost access to that third party email address, Microsoft and Google both have a process to allow you to update your security contact information, but you have to wait x days to allow the rightful owner to notice the change and cancel it, in case the change is made by non-owner. So perhaps these gaming services will have a process like that too.