Yes, there are some out there. You can start by looking on fanfic websites like Archive of Our Own. Just search for 'Death Note' and then filter for the gay relationship tags you're interested in.
The 'gay Death Note fanfic' is different as it often focuses on relationships and emotions in a way the original doesn't. The original is more about the cat - and - mouse game of justice and power. In the fanfic, there could be a lot of focus on how two male characters interact on an emotional and physical level. It might also change the pacing of the story. While the original had a fast - paced plot with new twists and turns related to the Death Note, the fanfic could slow down to explore the development of a relationship, with detailed descriptions of their first meetings, first kisses, and so on.
Archive of Our Own is a great place. It has a large collection of fanfics for various fandoms, including 'Death Note', and you can easily search for the gay ones using the tags.
Ryuk would probably just be amused. He is a Shinigami who has seen a lot in his existence. Fanfiction is just another strange human creation to him. He might chuckle at some of the more outlandish ideas in the fanfictions, like a character having superpowers beyond the Death Note.
Misa would likely be excited. She is a big fan of Light and the whole 'Kira' concept. In fanfiction, if there are scenarios where she has more power or a closer relationship with Light, she would be all for it. However, she might also get jealous if there are other female characters getting too close to Light in the fanfictions.
There is also a fanfic that reimagines the Death Note world with a gay subplot involving Near. It portrays Near in a different light, showing his vulnerability in a relationship. The fanfic cleverly weaves in the rules of the Death Note while exploring Near's character development within a romantic context.
Oh, for sure! Death Note is considered a masterpiece in the manga world. Its unique concept and the way it unfolds make it a must-read. The characters' development and the moral dilemmas presented make it stand out from the crowd.