Are there male and female watermelon fruits?
The referenced article claims that there exist female and male watermelons.
I think there are two ways of interpreting the claim of the existence of a male watermelon fruit.
male watermelon fruits are any watermelon fruits formed by male watermelon plants
or by the male reproductive units of watermelon plants.
some watermelon fruits contain seeds that all grow into male watermelon plants
1: Fruit of male
"In botany, a fruit is a part of a flowering plant that derives from specific tissues of the flower, mainly one or more ovaries." - Wikipedia
"n. pl. fruit or fruits 1. a. The ripened ovary or ovaries of a seed-bearing plant" - The Free Dictionary
"Fruits are produced only by flowering plants (angiosperms). Following pollination of the flower, the fertilized ovules develop into seeds while the surrounding ovary wall forms the fruit tissue, or pericarp." - Biology encyclopedia
By definition, males don't have ovaries.
Botanically speaking, a "male fruit" is a contradiction in terms
2: Fruit is male.
Plant sexuality is complicated.
In a few species, individual plants are either wholly male or female. In this case I believe the male plants do not produce fruit.
In many common plants, the individual flowers may be male or female (on the same plant) but the plant from which they emerge can not be said to be either.
Another way of classifying a fruit as "male" would be if the fruit were produced on a female plant but contained a single seed that would grow into a male plant. Since individual plants of some species can switch sexuality over time, the sex of an individual plant might not be wholly (or even partly) determined by the genetics of the seed from which it grew but by environmental influences on the growing plant.
As Quassnoi commented, Water meolons are monoecious - a single plant bears both male and female reproductive units. Therefore the plant itself cannot be considered either female or male. Therefore nether can the seed from which it grows or the fruit that contained that seed.
"The watermelon plant is a slender, sprawling, slightly hairy, monoecious annual." - Dewey M. Caron, Univ. of Delaware