Misunderstanding then on what the primary performance metric was.
As for the gaming benchmark, where am I getting my numbers from? Pretty simple math from the graphs in the hub at 12:19 in the first video.
In the first video the 1080p average the 7700x has an average frame rate of 218 frames, the 12700k has a frame rate of 187, so 218 minus 187 is 31 frame difference. 31 divided by 187 is 16.57%. Meaning, the 7700x is 16.57% faster in gaming using the HUB benchmark, see timestamp 12:19. If you go by the 1% lows in the same graph the 7700x is 175 and the 12700k is 147, so 175 minus 147 is 28. 28 divided by 147 means the 1% lows are 19% higher on the 7700x at 1080p.
The 14900k in the second video, see timestamp 18:59, for the 1080p shows an average frame rate of 158 and the 7700x is 138, so there is a 20-fps difference. 20 divided by 138 is 14.49%. You then take AMD's own slide showing 9700x having a median gaming performance advantage of 13% when compared to a 14900k.
So, to estimate the performance difference in gaming between a 12700k and a 9700x at 1080p
1 = 12700k.
1 X 1.1657 = 7700x (1.1657)
7700x (1.1657) X 1.1449 = 14900k (1.33) meaning the 14900k is 33% faster than the 12700k
1.33460993 X 1.13 = 1.5 or 50%, so in theory the 9700x will be 50% faster than the 12700k.
If we take the TPU benchmark results for the 14900k:
Intel Core i9-14900K Review - Reaching for the Performance Crown - Game Tests 1080p / RTX 4090 | TechPowerUp
The 1080p shows that the 12700k is 83.7% of the 14900. That is 17.4% slower compared to the 14900k or to put it another way 17.4/83.7 = 20.78% faster than a 12700k.
So, you take 1.2078 X 1.13 (9700x) = 1.3648 9700x, or 9700x is 36.48% faster than the 12700k
Either way you slice it the 9700x is going to be around at least 33%+ performance in gaming compared to the 12700k and could be as much as 50% if you use the HUB benchmarks for 1080p gaming 12 game average.