This gentleman gets it. The latter (unbolded) part though, unfortunate for you :(
The first set you mentioned is the standard Dual Screen Klefki; the latter though...I dunno, don't you think Klefki has better things to be doing than bulky boosting? Klefki shouldn't really be aiming to attack, it just attacks to do some damage whenever convenient, but Draining Kiss is a tad weak for a move for Klefki to simply throw out. Foul Play and Play Rough are the primary options because they can allow Klefki to do some damage in a pinch (Dazzling Gleam imo is inferior to Play Rough against targets like Tyranitar and Goodra); Draining Kiss may help Klefki to recover a bit but is too weak to matter much. Bulky boosting Draining Kiss sets would be better left off to stuff like Sylveon anyway.
I use the exact same set on my Syvleon, and it works Perfectly, I didn't try it on Klefki but since it worked on my slow Sylveon, I thought it work on this guy, well, after +2 SpA Klefki can definitely do something, the Klefki(s) I ran are: Swagkey (deleted it), Dual Screens (Replaced Swagkey), and weather starter (Rain dance, haven't fond a HA Politaod yet) the latter two are awesome and do the job right, the Swagkey seriously depends on luck which I lack. While Play Rough is certainly better than Dazzling Gleam (Except in Doubles IMO), Draining Kiss can certainly be useful as it's Klefki's only -while unreliable- HP restoring move, So I'd really use it and after 2 calm minds:
+2 0 SpA Klefki Draining Kiss vs. 252 HP / 0 SpD Tyranitar in sand: 128-152 (31.68 - 37.62%) -- 89.6% chance to 3HKO
With the recovery of Draining + Leftovers, Klefki can recover .. a lot, while 3HKO-ing Tyranitar, you are gaining a lot of HP. And for the +2 SpA, well it's really easy to set up with Prankster, if physical just use Reflect and Calm Mind, if special then directly calm mind. And again you'd be recovering 75% health of Tyranitar (Base 100 HP with full investment) combine that with Leftovers pls.
While on the other hand:
0 Atk Klefki Play Rough vs. 252 HP / 0 Def Tyranitar: 168-198 (41.58 - 49%) -- guaranteed 3HKO
Does more damage but does not really give you any HP back.
However Play Rough is more viable on sets that don't have calm mind