The performance may not be exactly 1:1 due to variations in how different manufacturers design things but for the most part, it is close enough.
Not really. As a good example, look at AMD's RX 580 compared to the GTX 1060, two cards that typically offer rather similar gaming performance on average. However, the RX 580 is around a 6.1 Tflop card in terms of FP32 performance, while the 1060 is around a 4.3 Tflop card. The RX 580 offers around 40% more FP32 compute performance, roughly on par with a GTX 1070, but that does not directly translate to typical gaming performance. That's a huge margin of difference, not at all what I would consider "close enough".
Likewise, look at what Nvidia had to say about the performance of these new cards. Going by quotes from the other article here...
In terms of performance, Nvidia claims that the GeForce RTX 3090 is up to 50% faster than the Titan RTX.
Nvidia touts the GeForce RTX 3080 as the flagship Ampere SKU. The chipmaker is promising up to double the performance over the previous GeForce RTX 2080.
Hmm... Let's look again at those Tflop numbers provided for the cards.
RTX 2080 = 10 Tflops
RTX 3080 = 30 Tflops
Titan RTX = 16 Tflops
RTX 3090 = 36 Tflops
So apparently, going from 10 to 30 Tflops only makes the 3080 "up to double the performance" of the 2080. And going from 16 to 36 Tflops only makes the 3090 "up to 50% faster" than the Titan RTX. If the "Tflop to gaming performance ratio" were similar, then the 3080 would be considered a 20 Tflop card, and the 3090 would be a 24 Tflop card, at least going by Nvidia's performance claims.
What this means, is that the actual gaming performance is likely around 33% lower than what these high Tflop numbers might imply. That would make the 3070's "20 Tflops" roughly comparable to the 13.5 Tflops of a 2080 Ti. That's still a good generational improvement, likely offering over 40% more performance than the 2070 SUPER currently available at that price point, but certainly not the more-than-doubling of performance that the Tflop number alone would suggest.