Sorry, but I cannot see a solution.
Although the Steam version and the GOG version of Tomb2.exe have exactly the same file size, the binary comparison using fc.exe shows some differences.
As already told, I can run TR2 from Steam perfectly, however the GOG version does not start visibly. After starting the GOG version, there is only a tomb2.exe process in the task manager, using ca. 14% of the CPU (i7-2600 - a Quad core with HT).
I stopped this process using the task manager.
For testing, I copied the Steam-Tomb2.exe into the GOG TR2-folder and tried to start TR2. This time, and error message appeared:
Microsoft Visual C++ Runtime Library
abnormal program termination
But again, the tomb2.exe process remained in the task manager.
After changing back to the original GOG version, the error message did not appear, and the Tomb2.exe again did not start visibly, but only as a process in the task manager.
Then I also installed nglide, but that did not help, either.
Strangely enough, Steam TR2 starts without problems when using the GOG tomb2.exe.
A quick note to the window problem I mentioned in my earlier post: Ther "Tomb Raider series fullscreen border fix" eliminates this behaviour, and with this fix installed, also the movies play correctly. http://community.pcgamingwiki.com/files/file/82-tomb-raider-series-fullscreen-border-fix