The Laughing mare herself is, as said by PoorYorick, the Element of Laughter personified. In In Nominé, however, that would also mean that she's a fragment of Harmony, Discord's counterpart. So she is quite powerful, but I'm not sure if she'd be strong enough to defeat one of "our" Gods. So the Demon itself wouldn't be a fight that could bring the God into "mortal danger", but it wouldn't be a pushover either. 

Eitherway, he hit himself with his own attack so him being pretty banged up while the Laughing Mare is incinerated is quite reasonable. Also, you described the "demon" as looking identical to Pinkie's corpse, so I assumed from the start that it was her alone which, now that I think about it, doesn't make sense as PoorYorick once stated that it would take six "Pillars of Joy" to bring her into the mortal plane... Powerful demon using Pinkie's corpse it is, I suppose.