While not that big of difference, the 14" is a little cheaper:
* The 14" MBP with M1 Max 10-core CPU, 24-core GPU, 32gb memory is $2,900
* The 14" MBP with M1 Max 10-core CPU, 32-core GPU, 32gb memory is $3,100.
The Mac mini with the Max variant chip will certainly be more than $1,000. But I expect it will be more reasonable than the MBPs, maybe $2,100 for the 32-core GPU version with 32gb of memory. That's how much the currently available Intel 6-core i7 Mac mini with 32gb of memory and 1TB of storage costs.
The point being that the cheapest 32-core GPU is $3,100, for competing with an RTX 3080 mobile that's constrained to about 105W (before it starts to pull ahead of the 32-core GPU in the M1 Max).
Overall it's just a silly premise that a sub-$1000 Mac Mini "would end up being the best gaming PC you could buy." That comment speaks to either not knowing the pricing structure here, or misunderstanding the performance comparisons.
A mid-to-low end desktop GPU pulls closer to 150-200W, and is not part of the comparisons here. And as Apple increases the performance of their chips, they also increase the price. So unless they start having 3 chips with the cheapest one being less than $1000 and massively ahead of desktop GPUs while pulling less than 50W, it's not going to happen. I don't see it happening in the next 5 years, and meanwhile Nvidia and AMD will continue their roadmap of releasing more powerful GPUs.
* The 14" MBP with M1 Max 10-core CPU, 24-core GPU, 32gb memory is $2,900
* The 14" MBP with M1 Max 10-core CPU, 32-core GPU, 32gb memory is $3,100.
The Mac mini with the Max variant chip will certainly be more than $1,000. But I expect it will be more reasonable than the MBPs, maybe $2,100 for the 32-core GPU version with 32gb of memory. That's how much the currently available Intel 6-core i7 Mac mini with 32gb of memory and 1TB of storage costs.