"People rush BotRK, but they don't rush Liandry's."
Well, yeah. That's normal.
First off, BotRK is actually not that often a rushed first-item. When it is, it's core to the champion (see also, Vayne).
Second point, BotRK and Liandry's build paths are separated significantly.
"Well, duh, one's AD and one's AP--"
No, no, no, listen to me.
Blade of the Ruined King builds out of Vampiric Scepter, a relatively cheap and often-considered core item to Marksmen, as Lifesteal is their main avenue of defense items. Once a champion has a Vamp Scepter, they choose between Bloodthirster (a more defensive option unless you have incredible AD ratios), Essence Reaver (niche pick with CDR and mana sustain), Zeke's Herald (hah!) and Blade of the Ruined King.
Liandry's Torment, on the other hand, builds out of Haunting Guise (Amp Tome + Ruby Crystal) and an Amp Tome. The base items--Crystal and Tome--are essential building block items for mages, but they provide strictly offensive or defensive bonuses, and have rather attractive upgrade paths that lead away from Guise and Liandry's.
Finally, frankly, while Liandry's is more than cost-efficient with its damage, it unfortunately doesn't feel like it's very powerful; plus, due to the "on spell hit" activation, it really only seems to shine when picked up by a DoT-focused mage, or one that casts spells frequently enough to refresh the DoT, but not so fast that it overrides the DoT.