Traditional dishcloths are generally made from microfiber or cotton. These are good for cleaning, but they are not very good at releasing liquid and dirt. Your cloth ended up being heavy and damp, and that's how odours have the chance to develop and grow.
Swedish dishcloths are made from wood cellulose and cotton fibers, so they function like a sponge and cloth. These cellulose sponge cloths absorb and quickly release liquid, thus allowing them to dry very quickly. Consequently, odours do not have a chance to develop, so they don't smell.