No, if you hold a valid VCP, you can do another VCP exam for different tracks without the official classroom requirements.---
Senior Infrastructure Specialist
The pages for each individual certification have "new candidate" and "existing candidate" tabs - you can use these to work out the correct path/requirements for you.
Path 2 under "existing candidate" will give you your answer on this page: VCP6-DTM Certification
And this is the best start page to find all the certifications: VMware Certification