A little more complicated than that, if you read the article. Once they have the (sterile) seedless watermelon plant, then they need to have a regular seeded watermelon growing nearby to pollenate it. But that still begs the question of where did the seedless plant come from.
That goes back to the horse/donkey example.
They use some kind of "chemical process" to prevent the chromosomes from dividing in meiosis. Thus instead of gametes (pollen and egg cells) with half the usual number of chromosome that will fuse together to create a (diploid) embryo with the usual number, they have gametes with the usual number, that will fuse together to create an embryo with twice the usual number (tetraploid). The tetraploid seed is grown out to a plant. A female tetraploid flower is then "artificially inseminated" with pollen from a regular diploid male flower. The resulting seed will have half the usual chromosomes from one parent and the usual number from the other and so will be triploid, 1.5 times the usual number of chromosomes. The triploid seeds grow into the seedless watermelon whose flowers then have to be pollenated with pollen from a regular watermelon to produce fruit.
But this process has to be repeated in each generation to get those triploid seeds. It's why they are rare.