To be fair, the standard bubble sort algorithm isn't vectorized, and so can only use about 5% of the power of a Cray-1. Which is good for another factor of about 5 in the array size.
Yes, as I understand it, its 80MHz clock gave it a 12.5ns memory access time, and I think it normally accessed memory four times per instruction, enabling it to do 20 MIPS (of 64-bit ALU ops). But the vector units could deliver 160 megaflops, and usually did. I think a TRS-80 could technically run about half a million instructions per second (depending on what they were) but only about 0.05 Dhrystone MIPS—see the Cromemco Z2 on https://netlib.org/performance/html/dhrystone.data.col0.html for a comparable machine.
So we can estimate the Cray's scalar performance at 400× the TRS-80's. On that assumption, Quicksort on the TRS-80 beats the Cray somewhere between 10000 items and 100_000 items. This probably falsifies the claim—10000 items only fits in the TRS-80's 48KiB maximum memory if the items are 4 bytes or less, and although external sorting is certainly a thing, Quicksort in particular is not well-suited to it.
But wait, BASIC on the TRS-80 was specified. I haven't benchmarked it, but I think that's about another factor of 40 performance loss. In that case the crossover isn't until between 100_000 and 1_000_000 items.
So the claim is probably wrong, but close to correct. It would be correct if you replaced the TRS-80 with a slightly faster microcomputer with more RAM, like the Apple iiGS, the Commodore 128, or the IBM PC-AT.
