Back in the low-res days of KQ1 and KQ2, the art in game manuals and on the box covers provided a better look at video game characters than anything the actual games could include. So naturally, Sierra's earliest KQ manuals were illustrated...
A vision of Graham appears in the Magic Mirror, KQ1 manual
Graham sees Valanice in the Mirror, KQ2 manual
...and according to their pictures, King Graham had a mustache. Wow.
However, believe it or not, Graham's upper lip hair actually seems to be drawn from fairy-tale illustrations--and one particular source.
Namely, that venerable Victorian fairy tale collection, Andrew Lang's Green Fairy Book. (Out of which Roberta fished, among other things, the names Lolotte, Genesta, Rosella, and Valanice, the three-headed dragon that feeds on tasty princesses, and the magical white snake which when eaten allows speech with animals.)
The original editions of Lang's Fairy Books (he wrote 12 in all, each with a different color in the title) were illustrated by Henry Justice Ford. Ford's illustrations in the early volumes (including the Green Fairy Book) are quite notable for the magnificent mustaches sported by the heroes in these stories.
Examples of this mustached-hero tradition from the Green Fairy Book:
Prince Vivien and Princess Placida
The Little Soldier
Prince Narcissus and Princess Potentilla
Other examples of heroic mustaches from HJ Ford's illustrations for Andrew Lang fairy tale books:
Bushy Bride, Red Fairy Book
Graciosa and Percinet, Red Fairy Book
The Master-Maid, Blue Fairy Book
The Gold-Spinners, Blue Fairy Book
The Iron Stove, Yellow Fairy Book
The Princess in the Chest, Pink Fairy Book
So what should we make of this? Quite possibly Roberta liked the vintage Victorian HJ Ford illustrations in Lang's books and asked artists at Sierra to copy their style for the KQ manual drawings. And it seems this extended to Graham having facial hair.
Of course, the KQ1 re-release box cover turned Graham into Prince Valiant with a mullet. But that's another story.