I would note, those figures look to be AV1 from Jan 2017. No idea what it looks like now as I haven't seen much news, but two years is a long time.
Honestly I don't expect AV1 to improve on quality, and I believe the bitstream has been frozen since the start of the year. Rather, quality will probably go down as they figure out how to cut down on the incredibly long encode times, so HEVC will likely remain the codec of choice for archival-quality stuff like Blu-rays. If we zoom-in however on the low-bitrate area, the advantages of AV1 are more apparent. This is from streamingmedia's look at AV1
from August this year.
The "Football" clip is supposed to represent the most challenging scenario (lots of detail, lots of fast motion). A VMAF quality of 93 is where the clip becomes free from visible artifacts and is considered the target. AV1 achieves that at a lower bitrate than HEVC (something like 2.05Mbps vs 2.7MBps).
Of course, the tradeoff right now is the incredibly long encode time:
At a factor of 45,316 x real time, current implementations of AV1 will take about 7 years+8 and a half months to encode a 90 minute movie on the reviewer's computer! (a Xeon E3-1505M v2) Even if we speed that up 8x (going from 2 cores to 16), and then x2 (from 2.8GHz to 5GHz+), it's still gonna take a hella long time to encode anything with AV1.
I understand that AV1 encoders right now are "reference" level, which basically maximize quality over anything else. Production encoders will likely dump some of that quality to gain speed, after which I suspect AV1 will lose a good portion of its quality advantage over HEVC, the remaining benefit being lack of royalties.