The only thing that is going to matter is supply, price/performance will work itself out. Intel's parts are aimed at (normally) low and mid range, we're talking 1650 super - 3070 levels (maybe) of performance.
It won't matter what Nvidia and AMD do if they can't get volume. Intel probably has volume, last year they used their TSMC allocation for HPC on the supercomputer Aurora, but not so much this year. This means they'll be able to knock out serious volume on that TSMC node. Volume is great for taking over market share in a supply constrained market like we have now.
My real point is, if the constrained supply issue dissipates - which it will if crypto crashes (and it seems to be trying to doing so) - that's when the performance\price will matter, when people have choices at relatively low prices.
If crypto shoots back up, then Intel will certainly have no issue selling all it can make at MSRP or higher.
Having said that, we're just talking about desktop dGPU here. Intel is releasing laptop based ARC dGPU, right now. Laptop is about 85% of the client market, no idea what % of the dGPU market it is though.
Nothing is decided here yet because we aren't there yet, but certainly I get the feeling Intel is blowing an opportunity, crypto seems very cyclical with a year or two of heavy gains followed by a couple of years of famine. Intel may wind up selling into the famine