It's been over a year now, but I've made some progress on this for my own setup, for whatever that's worth. I'm on Wine, but I think this should work for normal Windows installations, too. For me, Cyrem was on the right track about the Indeo 5 codec not being installed — it's just that the "Basic K-Lite codec pack" they recommended didn't work for me either. Instead, I figured out the instructions below.
For anyone trawling through old posts to try to fix this issue, here's the crash error message I was encountering every time a video would try to play (whether on game startup, winning/losing a race, or when viewing a boss intro video):
Runtime Error!
Program: [path]/LEGO Stunt Rally/_msr.exe
abnormal program termination
For Windows Vista and above, this codec are actually already built into the OS, it's just that the DLL containing the codec isn't registered by default. To register the DLL containing the codec, type or copy/paste each of the lines below (minus the "C:/> " portion) into an elevated (Administrator) command prompt. PowerShell works, too.
(only enter the first line if on a 64-bit system, otherwise skip to the second command)
C:/> cd C:\Windows\SysWOW64
C:/> regsvr32 ir50_32.dll
If you need to unregister the DLL containing codec for any reason, you can enter the following commands:
(only enter the first line if on a 64-bit system, otherwise skip to the second command)
C:/> cd C:\Windows\SysWOW64
C:/> regsvr32 /u ir50_32.dll
For Windows XP and below (useful for when using a VM or Wine), you'll need to install the codec from free-codecs.com and use the "typical" install option. I know the website name sounds sketchy as hell, but apparently it's a semi-official repository for this codec? Regardless, it's the only one that really worked for me, and it didn't install any crapware — just the intended codec. I tried other installers from other sites, but they kept getting stuck on the "searching for Netscape installations" (lol). So take that as you will.
I also ended up using the alternate installer that someone created to work on more modern systems (works on XP and above), but I don't think that had much to do with my success here. This also automatically adds shortcuts that don't require the CD, if that interests you at all. If you do opt to use this installer, know that there's a minor bug that can make it fail to copy "dsetup.dll" from the install media to the application folder on the hard drive.
After doing the above, I was able to launch the game without needing to use /NOINTROVIDEO — since the game no longer crashes when trying to play a video.