It seems some cards in Classic format have accidentally gotten the Undead tag, for example Spiteful Smith and Kidnapper.
Seems like an error, especially considering some other Undead are still untagged in the format, like Sylvanas and Bloodmage Thalnos, and it obviously wouldn’t even make sense for them to have the tag when everything’s supposed to be like how it was in 2014.
Also Wild Pyromancer. The obsevration is spot-on, though! 
Well, The Beast isn’t, although Illidan is. Besides, the arts for some cards have been changed.
I don’t think the tag in question has any implications in terms of game mechanics, but it is at least a cosmetic issue nonetheless.
Considering some of the art isn’t returned to their original state, it already fails to be perfectly ‘like it was in 2014.’ The new ‘classic’ logo isn’t the same as the original as well. So, it’s not like this is the only non-2014 difference in the format. It doesn’t affect the game and non-2014 portraits can be used to. So it’s just kinda silly to point out the undead tag thing.
Most importantly, Jaina’s original portrait — forgot to mention that, by the way. 
Which is actually a good thing, if you ask me, and some of the new arts are fine, too.
Or maybe it is a comment like this that is silly?
The issue in question is a symptom of the developers’ sloppiness, them having missed an obvious inconsistency, and even if it ‘doesn’t affect the game’ at the moment, such approach in general doesn’t bode well at all, since bad practices likely underlie problems like this. I actually appreciate the mistake’s having been pointed out.
From 26.2 Patch Notes :
[Hearthstone] Corrected typing for Wild Pyromancer. It is now an Undead in all formats except for Classic (where there are no Undead—sorry, Sylvanas).
However, the Spiteful Smith and Kidnapper still are.
Can’t even fix something this simple completely and properly, eh?