What is a 21q21 deletion?
I would suggest looking more into karyotype nomenclature; it is admittedly a bit odd. Here is one related question/answer that puts it in context.
I haven't looked at the paper in detail but generally what it means is that there is some cytologically relevant big chunk of chromosome that is missing that roughly overlaps with the chunk of chromosome that we find at band 21 of chromosome 21 (not position 21). Note that these cytobands/karyotype/G bands visible in a chromosome spread under a microscope, so these are quite large deletions.
Looking at the paper methods, it is clear that in 2/3 cases they confirmed the deletions by looking at karyotype data (FISH/chromosome spreads):

For Case 2, CNV confirmation and parental studies were performed by metaphasic and interphasic FISH on leucocytes using BAC RP11-43A6 (chr21:18,414,905e18,567,253, hg19 build). For Case 3, CNV confirmation was performed by G-banded karyotype. Parental studies were not available.

The terminology is quite outdated now as usually we are looking at sequence data these days, which has much higher resolution, but a lot of the stereotypical chromosomal abnormalities still carry these confusing names. And seeing it on a chromosome under a microscope is still the gold standard for these large chromosomal events.