Thirsty Sword Lesbians is obviously using queer centric high-drama fiction as its root, with a dash of Monsterhearts mixed in for move inspiration. It's all about being turned on/off, messy drama, sword fighting as ways to find out people's true feelings to draw strings on them, and dives into the sort of "oh no they're really hot" villain stuff where the GM can use involuntary attraction as a potential move downside. It's a very melodramatic game, and so the romances it's going to create through its mechanics are similar.
An example of how it structures the conversation is the core "Heartstring" move Entice:
When you appeal to someone’s physical or emotional sensibilities, roll +Heart:
10+: Gain a String on them and they choose 1
7–9: Gain a String on them, unless they decide instead to choose 1
- Get flustered and awkward
- Promise something they think you want
- Give in to desire
Under Hollow Hills is a game about relationships, but without an implicit conflict model like Monsterhearts/TSL. It's also about faeries (mostly), so you get a bunch of gorgeous fantastic high-romance nonsense like this move from the Nightmare Horse:
When you take someone’s breath away, roll. On any hit, your eyes meet and they catch their breath. They can’t proceed with what they were doing until they’ve answered you. On a 10+ hit, choose 2 of the following to say, and you’re telling them the truth. On a 7–9 hit, choose 1.
•At this moment, for me the moon rises and sets in your eyes. Will you close them against me?
•At this moment, at any other soul’s approach but yours, I would flee. Will you come closer?
•At this moment, no one but you may touch me in safety. Will you?
•At this moment, I will bear no one on my back but you. Will you ride me?
•At this moment, I’m wearing my silver necklace, and if you place your hand on it, I’m yours. Will you?
•This moment is fleeting and there is no other like it. Another instant and I may never be yours. Will you come to my arms?
It also has a set of "obvious plays" like
Draw Someone Out, Open Up to Someone, Put Someone Off, etc - that are all built to interrogate and establish/deepen/curtail interpersonal relationships between characters.
MF0: Firebrands is very explicit that each system is its own game. One of those, for instance, is A Dance, which is a conversation about the sort of very intimate things that might happen in the context of a high-drama ballroom, with questions you can choose pose each other like:
- The dance’s figures separate us. When they bring us back together again, do you blush?
- You may, at this moment in the dance, place your hand upon my elbow, my shoulder, my waist, or my hip. Which do you choose?
-This moment in the dance allows me to step close to you and linger very near. Am I welcome?
There are some other games that do similar things, but one key about all of these is that in the moment the onus is always on the "target" of a move to choose the outcome. The Bakers are especially big on preserving PC vs PC consent in their core design (you see this in AW's Go Aggro, etc as well), and the designers of TSL keep that in mind too. It's on the target of Entice to decide if you're appealing to their physical or emotional sensibilities before any mechanical outcome can proceed.
So if you want to design rules to push the shared conversation towards romantic implications, I think that's a pretty important thing to keep in mind. Most game designs don't really support that sort of structure, or build it in, so I think mechanical support for relationships writ large much less ones that can get as complicated or easily messed up as romantic ones is left pretty absent.