By definition this was the best I could find:
H.263 is a video codec designed by the ITU-T as a low-bitrate encoding solution for videoconferencing. It was first designed to be utilized in H.324 based systems (PSTN and other circuit-switched network videoconferencing and videotelephony), but has since found use in H.323 (RTP/IP-based videoconferencing), H.320 (ISDN-based videoconferencing), RTSP (streaming media) and SIP (Internet conferencing) solutions as well.
H.263 was developed as an evolutionary improvement based on experience from H.261, the previous ITU-T standard for video compression, and the MPEG-1 and MPEG-2 standards. Its first version was completed in 1995 and provided a suitable replacement for H.261 at all bitrates. It was further enhanced in projects known as H.263v2 (a.k.a. H.263+ or H.263 1998) and H.263v3 (a.k.a. H.263++ or H.263 2000).
The next enhanced codec developed by the ITU-T (in partnership with MPEG) after H.263 is the H.264 standard, also known as AVC and MPEG-4 part 10. As H.264 provides a significant improvement in capability beyond H.263, the H.263 standard is now considered primarily a legacy design (although this is a recent development). Most new videoconferencing products now include H.264 as well as H.263 and H.261 capabilities
I have a feeling that H.263 may have been dropped in favor of H.264
In all the tests I ran the error was "could not find encoder" VLC is a major proponent of H.264 and it works well with the MP4 container.
I believe this was supported by ffmpeg a module VLC uses for a variety of formats including DivX, XviD, WMv 1-2 etc.
Another clue is that Preferences shows all of the compiled modules and I can't find a reference to H.263 only H.264
I doing a search of VLC websites I find that playback is supported for h.263 in all operating systems but can find nothing about the encoder.
So unfortunately is is going to take a developer to answer these questions.