You guess it right. It is just as simple as changing the primaryEmail field. Here is my example below:
Let's say I am a reseller from reseller.com, and I have a resold domain called resold.com. Currently, I have one user created in my resold domain with the email address emily@resold.com. I am going to update it to happy@resold.com. Note: I am using my reseller reseller.com's credential.
PUT /admin/directory/v1/users/emily@resold.com
{
"primaryEmail": "happy@resold.com"
}
HTTP/1.1 200 OK
{
"kind": "admin#directory#user",
"id": "XXXX",
"primaryEmail": "happy@resold.com",
"name": {
"givenName": "Emily",
"familyName": "Lam",
"fullName": "Emily Lam"
}