First off that's not a watermelon. It's a Cucurbita sp.
That is extreme nitrogen deficiency. It needs a big dose of fertilizer.
Transplanting watermelons and other cucurbits is highly effective if done correctly. It's commonly messed up.
First off you should only start them 3 weeks before you want to transplant them. It takes 3-4 weeks for most cucurbits to be ready to transplant.
Week 1: Seed and allow to to germination at around 80F.
Week 2: Fertilize and first true leaf should emerge. If the cotyledon turns yellow, it's under-fertilized.
Week 3: They need to go outside for hardening off. The 2nd true leaf should develop
Transplant: They do best when transplanted at 3rd-4th true leaf. Plant them so that the cotyledons are level with the soil surface. Transplanting larger plants increases transplant shock and slows down their development.