While that razor is a real "Damascus" razor, it is not what you are thinking of wrt pattern welded or (if there really are some out there) wootz steel razors.
Bear in mind that with vintage razors the technology for making Wootz was as it were lost. Makers would use the name "Damascus" as a trademark or to imply a particular blade was supposed to be better. It has only been in the last 50 years (or less) that pattern welding has been rediscovered, along with some of the metallurgical secrets of Wootz that had been lost.
I'm sure there are a few here who could give you even more detailed information.
In a nutshell, the razor is not a fake. It is old and "Damascus" is simply the name of it. When the razor was made, nobody knew how to make "real" Damascus anymore.
Hope this helps.
John P.