Looking at this list it's hard to see how he doesn't belong, among the starting pitchers he's 1st in SO/9, 2nd in BB/9, 2nd in SO/BB, 3rd in ERA+, and 5th in WAR.
I think two things work in Greinke's favor here - Steve Busby's inclusion and his 2009 Cy Young season. Busby had a promising career derailed by injuries which limited him to just three full seasons and 1060.2 innings. His two no-hitters and 22 win 1974 season were the obvious factors in his induction.
As for 2009, it is the best pitching performance in franchise history and while that in itself isn't enough for induction Greinke had three other seasons with an ERA+ of 120 or higher. To recap here's where his 2009 ranked in Royals history in various stats:
ERA+ - 1st (205)
WAR - 1st (9.0)
SO's - 2nd (242)
SO/9 - 1st (9.50)
Something working against Greinke is the absence of Charlie Liebrandt. Liebrandt also had a 116 ERA+ in his Royals career to go along with 76 wins. Considering he's one of the heroes of 1985 I'm actually quite surprised he's not in.
While in the process of writing this post I noticed Nick Scott has a Greinke article up at Royals Authority focusing on Greinke's place in team history. He argues against his inclusion due to lack of longevity, which is fair I think but again Busby's in, so there's that.
Personally I think he deserves to be in but his request to be traded will ultimately be what keeps him out. A graceful exit it wasn't and comments he made after the trade didn't exactly endear him to Royals fans. I don't consider him a no brainer though so I won't consider it a travesty if he never makes it.