I have been trying to get this working today and have managed to find a workaround. The reason why the in-game videos do not work but the intro videos do is because it is trying to play the game videos at a different resolution (and possibly using a different codec or something). I have found a way to tell it to play the in-game videos at a lower resolution using command-line parameters. The videos don't look great but the audio works so it is at least playable. I don't know how used to dos you are so I will talk you through it.
1.Load DOSBox and mount your folders as normal. Navigate to the city2000 folder.
2. type 'cd london' and hit enter.
3.If you are playing fullscreen then type 'lonexe /sf /v1 /w1' and hit enter. If you are playing windowed type 'lonexe /sf /v2 /w1' and hit enter.
This will run the game minus intros but the video should run. For an explanation of the v and w parameters type 'lonexe /?'. Essentially, specifying v0, v1, v2 or v3 you select one of four video modes for the game. v1 and v2 are low res and v0 and v3 are hi res, with v1 and v3 scaling to half screen width which looks better in fullscreen mode. v0 is the default which the game normally runs, but for dosbox you need v2 or v3. (specifying w0 will also stop the annoying wipes when you move around in the game).
If you want to be able to load the game in the normal way (i.e. by typing 'london' as normal) then do as follows:
1.Open windows explorer and navigate to the 'city2000' folder.
2. Open the 'london' folder.
3. Right-click 'london.bat' and click 'edit'. This should open the file in notepad.
4. Locate the line 'lonexe /SF /V0 /W1'.
5. Type 'REM' at the beginning of the line so that it now reads 'REM lonexe /SF /V0 /W1'.
6. Add a new line below that one and either type 'lonexe /SF /V1 /W1' or 'lonexe /SF /V2 /W1' depending on how you want your video to look (see above for the difference).
7. Click 'File | Save' and exit notepad.
. Return to DOSBox and type 'london'. After the intros the game should load with working video.
Let me know how you get on.