The H.264-encoded variant of the clip uses about 1 Mbit/s, which is not a terribly high bitrate, but it's also not nothing. You can get by with 1.5 Mbit/s for H.264-encoded video at 1080p, if you use a good encoder and you configure it properly.
There are several factors that come into play here:
The video is not actually 1080p. Its dimensions are 1920⨉804, so it's closer to 720p vertically.
YouTube can use a very slow and compression-efficient encoding process, since it's better for them to invest into encoding for quality once, using their parallel cloud services, and later stream reduced file sizes. The encoding will only cost them once, but the streaming will cost them multiple times — think of thousands or even millions of streams. Other VoD companies like Netflix are doing the same.
Generally, animated content like this is not super hard to encode. It lacks high-frequency camera noise or simulated film grain (which is hard to preserve while encoding) and you will often see smooth surfaces.
The content includes a lot of scenes with a completely static camera, where motion is constrained to only small parts of the video (i.e. moving objects or protagonists). Such motion can be easily predicted and encoded with B-frames, where the majority of macroblocks in the frame can be skipped entirely. This saves bits.
Finally, I'd say the quality is okay — it's not perfect. You can still see color artifacts and smudging in areas with high spatial complexity (like fur), and these aren't perfectly sharp either.
The VP9-encoded variant (which you will see when using Google Chrome) uses about the same bitrate, but its visual quality is much better, as VP9 is a more compression-efficient codec. Compare a screenshot of the H.264 version (click to enlarge) …
… against the VP9 one:
You will see much more spatial detail in the fur.