According to one site, in Daggerfall it is possible for the random quest generation mechanism to create a quest storyline in which two NPCs are in a same-sex relationship. If you have any screenshots or videos with examples of this, please get in touch.

LGBTQ references in this game series:

The Elder Scrolls II: Daggerfall (1996): Jaciel Morgen and Deyanira Katrece

An Elder Scrolls Legend: Battlespire (1997): Pun/joke about the Khajiiti Navy; NPC same-sex spouses; Lord Killbar

The Elder Scrolls III: Morrowind (2002): Vivec; Uncle Crassius Curio; Argonians; Daedric Prince Boethiah; Mephala; Molag Bal; Buoyant Armigers

The Elder Scrolls V: Skyrim (2011): Bjornolfr and Hrodulf, Same-sex Relationship Options

<games listed below are still being researched>

The Elder Scrolls IV: Oblivion (2006): Ahzirr Trajijazaeri; Viranus Dolton and Eduard Hodge; Dumag Gro-Bonk; Pelinal; City-Swimmer

The Elder Scrolls Online (2014): Bameli the Pure; Hadrill Diina; Jakarn; Arlie Edrald, Frederick and Dulkhi; Make-Many-Waves and Sendrasa Llarys; Goveled Herendas; Captain Linwen and Faenir; Hartmin and Mirllir; Snaehild; Sind and Tand; Davilia Ralas; Captain Rana and Sargeant; Seyne; Erirus Cine and Therich Roielle; Little Leaf

See also QRM’s entry for this game.

Citations:

1. Lady Nerevar. LGBTQ in the Elder Scrolls (n.d.). Retrieved from http://ladynerevar.tumblr.com/post/92855271360/lgbtq-in-the-elder-scrolls
2. Other Quest Givers. Daggerfall: Quest Related Hints. (n.d.). The Unoffical Elder Scrolls Pages. Retrieved from http://www.uesp.net/wiki/Daggerfall:Quest_Related_Hints