Two options:
1-Use a capture card (you can of course send the replay file to someone else who has a capture card).
2-Doable by yourself with a USB stick (for Halo 3) or without needing one (for Reach and 4): frame-by-frame screenshot the clip in replay mode and extract the images. The upshot is that you get downsampled-from-4K 1080p (albeit jpeg'd) (and no motion blur) footage of the games, the downside is that it's a pain in the ass.
Kind of what I thought, a bit complicated. I'll look into it though. If there was one "pie-in-the-sky" type feature I'd like out of future Halo titles it would be to at least somehow better integrate the Xbox infrastructure with PC/internet in ways like this.