What skills would you define as "Courtly Skills"?

My take:

Compose
Courtesy
Dancing
Fashion
Flirting
Intrigue
Orate
Play
Recognize
Romance
Singing

Questionable but possible:
Gaming
Heraldry
Tourney

What are you getting at? Do not understand the question, or why it is important ;)

I guess it has to do which ones of them might benefit from a bonus from Glory?

Interesting thing is that KAP 5.1 only lists out three skills with that Special bonus from Glory:
Flirting & Orate may have +1 for each 1000 of your own Glory.
Heraldry gets +1 for each 1000 Glory of the person whose heraldry you are trying to identify. Curiously enough, Recognize doesn't get this same bonus (I'd argue that it should, since it specifically says that you'd be more likely to remember the best knights in a tournament).

However, p. 105 talks about Glory Skill Modifier, and lists out Singing, too, and talks in more general terms about courtly skills. I actually dislike this Skill Modifier a lot, since it destroys niche protection. The glorious knight becomes the BEST at everything at court, thanks to his Glory Skill Modifier. So I don't use it in the campaigns I GM.

Other than that, and the point that Recognize should be treated like Heraldry (i.e. the bonus depends on the other person's Glory, not your own), I think Gilmere's list is OK. I would not give the bonus for Gaming nor Tourney.

My view:

The bonus for Recognise and Heraldry skills applies to other peoples' use of the skill, not the Knight with the Glory: high Glory makes your blazon and face more widely known.

Gaming and Tourney don't qualify for a Glory bonus. Having someone throw a game of Hafntafl, or get you a better draw in the lists is better covered by Intrigue/Folk Lore and roleplay, IMO.

Compose won't qualify either: doggerel remains doggerel. While sycophants might praise a high Glory author no matter how turgid his prose, or lifeless his melodies, the mechanic is aiming to produce an "objective" level of success. I think this applies to Play and Sing as well, since it's the quality of the execution that's at question. Similarly with Dance.

The bonus for Orate, by contrast, can be rationalised by the Orator trading on his reputation as a mighty/influential knight to make his forceful point. Anyone can roar and bluster, but when a survivor of Badon speaks, everyone listens (even if he's a terrible old blusterer).

Given that the income per year of a Lady influences the value of the Amor/Love Passions that her Lover(s) acquire, it certainly seems entirely reasonable for there to be a ref-qualified Glory-based bonus to some rolls on both Flirting and Romance.

Fashion filters down from above; rank should add more of a bonus than Glory. But it's certainly arguable that in a smaller pool, a more respected Knight's mode of attire might sometimes be considered more Fashionable than some Johnny-come-lately stripling, but that's more a function of implied closeness to the seat of power, and good old Sir Stanley d'Ard come straight from Camelot to the North might carry the same influence on style as Gawain. More a circumstantial bonus than purely Glory-based.

Courtesy and Intrigue might sometimes have bonuses from the Glory of the manipulator, but possibly only based on the difference in Glory between the actor and the target of their skill use. Or even be a flat bonus for being more Glorious. Other times there might be a penalty: folk will remember Lancelot asking questions, after all...