Jason - There are two railway bridges running from Manchester across the river to Richmond. I believe pictured on the postcard is the one just north of 14th Street.
On the postcard two easily identifiable Richmond buildings are the State Capitol building and the old City Hall. The tallest building in the photo is the new City Hall, which will help as a reference point.
On the following map I placed red sight lines for the postcards image using the buildings and railway as reference points. Of course we can move the vantage point north or south on the Manchester shoreline, but it won't have a drastic effect. That is unless we move it so far that the image itself would be completely different.
Further south on the map is a red box. This is the location of tobacco row in Shockoe Bottom. Based on the site lines I believe you will see how it's not possible for those buildings to be pictured in the postcard.
Here is a photo I took today from the 14th Street bridge. Notice it is looking across the river turned slightly north. The new City Hall and railway are visible in similar positions as on the postcard.
This is a photo from the opposite side of the bridge looking back at tobacco row. Notice how much further south down the river the angle is. The tallest smoke stack on the right still has Lucky Strike painted on it.
One of the most iconic Richmond Landmarks is Main Street station. If the postcard image included both the Capital and tobacco factories in the Bottom, Main Street Station would be right between the two. Anyone ever traveling north or south on 95 through Richmond has driven right past it.
I have not definitively identified the address of ATC Factory #25. Finding any documentation that uses this factory tax number is difficult. The period addresses for ATC factories in Richmond that I have found are located within the red box on the map.
I do love the Richmond postcard and want to do some more research on some of the buildings pictured in it.