さしあたって、以下のように Defaults requiretty をコメントアウトすればよい。
## Disable "ssh hostname sudo", because it will show the password in clear. # You have to run "ssh -t hostname sudo". ##Defaults requiretty
## Disable "ssh hostname sudo", because it will show the password in clear. # You have to run "ssh -t hostname sudo". ##Defaults requiretty