Not really Gen hinted lightly but never mentioned Tess just that he should get married and Anduin sais "I'll do it for love.". Genn then basically dropped it.
Here lies the problem Anduin as king basically just in medieval diplomacy just gave Genn a big "Fuck You." a king does not have that luxory of marrying for love. Marriage for royalty basically up until WW1 was purely political. Sometimes love blossomed (Victoria and Albert) but most of the time, yeah Love wasn't a thing that mattered. Make an heir and now, make sure both sides are royal, if not possible a child of a Lord.
Genn should be pushing Anduin to marry Tess. "What a King must do." includes producing a legitamet child or full royal blood. Tess is the only true option, if negotiations between Stormwind and Gilneas failed Taelia being the daughter of Bolvar, a lord of Lordaeron and was regent when Varian was missing presumed dead is the only other in game character that would be acceptable to the other lords due to her bloodline.
If Jaina was younger she'd also be acceptable to the lords (Throw away auntie Jaina for a moment.) due to her position as Daughter of the high admiral of Kul'tiras and former position as leader of Theramore and Dalaran respectively. But she's beyond now what would be considered by pre modern standards Child bearing age.
(Just a note out there, lower classes were not marrying for love either, it was also purely business ventures between families. Usually somewhat related as in Father of one child looking at his cousin who is of similar age to child and go "That's your spouse and we both get some nice things out of it. Now produce grandchildren that will be working the fields.")