Author says that the BPG version is re-encoded from the MP4, so lower quality is to be expected. Looking at the linked comparison tool[1], it seems that while BPG and WebP both have fewer artefacts than JPEG at a given file-size, BPG seems to achieve this with waaaay too much smoothing. Seriously, check out the engineer's eyelids in [1].
I take your comment to mean that you find the BPG version of that engineer picture -- being "overly smoothed" -- to be unrealistic, comparatively. I think the face, as a whole, looks crisper. Even though the sharpness isn't there, the lack of visible artifacts just looks plain better. This reminds me, weirdly, of seeing video through an old television. The resolution is poor, but it's not poor in a way where I think the image is fake. Things still look real.
Separately, though, take a look at other features of the image: the beams running lengthwise down the shell, specifically the ones on the top left of the image. The BPG version makes them look niceeeeee and crisp, whereas the WebP version looks very bad.
Other places where I think the BPG compression looks noticeably better: her uniform (right sleeve, right leg, etc), the rivets along the top edge of the platform she's standing on, where she's grabbing that power tool.
One thing I noticed in the BPG version is that some gradient areas have more visual banding compared to the WebP version.
