The process you currently have depends on a drop down list selection on the record. This selection is filled in before you first hit save on the records so the process knows exactly where to go.
When you log your record through an email this drop down list will not be filled in and so it will automatically go through the NO route on your decisions and most likely directly land on the Resolved Status.
So to work around this I would suggest adding in a new decision in the beginning of the process which will ask if the Incident was logged with an email or not? If it's logged with an email you can have the record land on a new status, for example called: "Email". You can then create a query / workload list for your analysts to see all incidents on this status, where they can fill it in and manually select Incident or Request.
A decision for this could for example look at the "creator user" as any Incident logged via email will status the user used for your Inbound Mail Service.
I hope that helps.