Tested again, this time with the browser shutdown. It worked, bringing up
https://www.classicube.net/acc/register/. Once SeaMonkey was running, tried again, new window with
about: once again came up.
Noticed that when I started ClassicCube from a command prompt, the prompt output was,
F:\games\ClassiCube>ClassiCube.exe
Starting ClassiCube 1.3.6 ..
Adding http://cs.classicube.net/client/builds.json (type 0)
Fetching http://cs.classicube.net/client/builds.json (GET)
HTTP: result 0 (http 200) in 322 ms (94 bytes)
Going back to sleep...
Going back to sleep...
DIVE is disabled - Panorama's shadow-buffer is enabled
[calBackendLoader] Using libical backend at Z:\mozprofiles\Mozilla\SeaMonkey\Profiles\2nf8z26q.new\extensions\{e2fda1a4-762b-4020-b5ad-a41df1933103}\components\libical-manifest
DIVE is disabled - Panorama's shadow-buffer is enabled
Closing ClassicCube left the cmd prompt looking like it was still open and when I pressed CTRL-C, not only did ClassicCube finish closing, so did SeaMonkey.
On the command line, entering "seamonkey
https://www.classicube.net/acc/register/" works as expected, new window opens with the page loaded.
Seems like DosExecPgm needs something like "start" to have a new instance of the browser.