Thanks to prodding by the endlessly patient Bruno and less so Wagner, the problem and solution is this:
Problem:
Running a Webcore app from Delphi resulted in an error.
Solution part 1
The path and endpoint has to be reserved in HTTP.SYS. This is done using one of a number of provided tools: I used TMSHttpConfig.
Looking at the log on the TMSWebserver (when I tried to run the program), it told me that I had to reserve: http://+:8000.
So using TMSHttpConfig, I did.
Problem 2
now running the program in Delphi gave me a 'the process cannot access the file because it is being used by another process' error.
Solution Step 1
I used a free port scanner called SolarWinds, and scanned ports 8000-8010 on my local IP (192.168......).
This shows me that 8000 was in use by 'irdmi' - a pre-installed service 'Intel Remote Desktop Management Interface', probably preinstalled by the IT company that put the machine together.
8001, 8002, 8003 were also in use. 8008 is http-alt.
Anyway, 8010 was clear.
Step 2
So, using THMHttpConfig, I removed http://+8000 and setup http://+:8010 with rights granted to 'Everyone'.
In Delphi Tools|Options|TMS Web, I changed port in the URL entry from 8000 to 8010.