I verified that Reusable Content is available for Content Editor Web Part also. Please ensure following:
• You have enabled publishing infrastructure or start with publishing site template.
• Ensure Reusable Content list is created at root web level
• To use it in rich text field of SharePoint site, the publishing features must be enabled at sub sites level too.
• If you are using rich text field (and not CEWP), also make sure the rich text field you have is "full HTML with Formatting and constraints of publishing"
UPDATE:
I also found that it will be enabled only when you are using the field: "full HTML with Formatting and constraints of publishing" Or you insert HTML Editor web part (I assume Content Editor Web Part) inside above field while editing. So I think ultimately it boils down to the fact that it is enabled only when you are editing content of a field: "full HTML with Formatting and constraints of publishing"