So Downs syndrome is actually the opposite, they have an extra chromosome on chromosome 21. I think the only disease caused by a missing chromosome is Turners disease, which is caused by an almost not there X chromosome.
There are some gender related conditions caused by other chromosome/gene problems. Hemophilia is a disease where the blood cannot clot properly, because the proteins needed to do this are missing. It is due to a gene found on the X chromosome which is faulty. It affects males more, because they have XY, so if the X that they have carries the faulty gene, they will get Hemophilia. However, because girls are XX, they get two copies of the X chromosome. If they get one fault copy, the other non-faulty chromosome compensates, and they wont get the disease. Only if they get two faulty X chromosomes, will they get Hemophilia, and that is very rare.
There are no diseases on the Y chromosome, but there are a few on the X chromosome. You can also get too many sex chromosomes, and be XXX, XXY, XYY. These results in some abnormal sexual characteristics, or can just be fine
Missing a chromosome can cause all kinds of problems (depending on the chromosome), but gender is related to a specific pair of chromosomes, the sex chromosomes (which are either XX or XY).
You can have genetic diseases on the X and Y chromosomes (giving you diseases that are sex-linked (in science called X-linked)), so Downs syndrome is related to one pair of chromosomes, whereas X-linked diseases are linked to the sex chromosomes