The .heic format now used by iPhones is the same idea (https://en.wikipedia.org/wiki/High_Efficiency_Image_File_For...). But wider use of that is going to be constrained by the cost problem HEVC has in general (two patent pools to deal with). Some of WebP is based on VP8 (not VP9) intra coding too.
There are a lot of tools packed in AV1's intra coding (and HEVC's, though I've read less about that). Block sizes range from 4x4 to 64x64 and there's a mix within one image, so the encoder can use the right size for the level of detail in each area. There are more ways to predict a block's content from what's to the top and left, which leaves less work for the JPEGish DCT part. There's clever de-ringing post-processing that, in effect, blurs away many of the attention-getting JPEG-y DCT artifacts around edges, while 1) being aware of the direction of the main edge itself to avoid blurring that away and 2) using contrast thresholds to preserve as much other legitimate detail as it can--more about deringing at https://people.xiph.org/~jm/daala/deringing_demo/ .
(There's some good detailed discussion at https://parisvideotech.com/wp-content/uploads/2017/07/AOM-AV... and in Wikipedia's page at https://en.wikipedia.org/wiki/AV1 )
Relatedly, given the complexity, I wouldn't expect this to, like, take the world by storm in the next three months. The unoptimized encoder is still _really_ slow. Google has designed a hardware implementation, but of course hardware designs take time to get integrated, fabbed, and into shipping products. Given who's involved, I'm hopeful it does get wide support. (Would love to hear Apple's plans given their current support for x265; their decision to join AOMedia is a good sign at least.) Anyway, looking forward to seeing the results.