I figured that one tube is stretched by the gravitational waves and the perpendicular tube is unaffected, so you're measuring the difference between the two tubes. Simple and easy to understand. However, the video mentioned that both light and the detection apparatus are stretched by the same degree and the physicist says "the light does get stretched and that part doesn't do the measurement for us"[1] -- which makes me think that the simple and easy explanation is not quite right. There's some subtlety that I think I'm missing.
[1] https://m.youtube.com/watch?v=iphcyNWFD10&t=376s (6min 16sec into the video)