If you own a valid license of Vulcan.NET, then you can distribute a certain set of assemblies (DLLs) with your application.
These assemblies are documented in the Vulcan.NET documentation and a list of these assemblies can be found in the file redist.txt which is located in the Redist folder inside your main Vulcan.NET installation folder.

Nowhere in the Vulcan.NET license it is stated that these assemblies must be used from an application compiled with Vulcan.NET.

In fact, the Vulcan.NET documentation even has a complete chapter called "Using A Vulcan.NET Class Library From Another .NET Language" which describes how you can use a Vulcan.NET class library from another .NET language and which problem you may encounter when you do so.

All the X# compiler does, when you compile your application for the VO or Vulcan dialect, is follow these rules.

Some of the things that are written in this particular help file chapter do not apply to X#:
the documentation states that "no .NET languages other than Vulcan.NET understand the semantics of the USUAL or DATE types".
That was probably true at the time that the documentation was written. At this moment however this is no longer true.
The X# compiler translates the XBase types ARRAY, DATE, CODEBLOCK, FLOAT etc into the appropriate types which are then found in the Vulcan.NET runtime assemblies.