4e has lots of grids for resolving combat. So does the AD&D DMG. Given that 5e uses 5' increments for resolution, it could too.
I don't really see how these issues of presentation bears upon whether or not it's a RPG.
The core of a RPG, it seems to me, is that (i) the fiction matters to the resolution, and (ii) the non-GM participants (ie "players) engage the fiction predominantly from the first-person perspective of characters in the fiction.
(i) is what differentiates a RPG from a boardgame. (ii) is what differentiates a RPG from a free kriegspiel-eseque wargame.
No doubt there are marginal cases that are RPGs but don't quite fit (i) or (ii), or that fit (i) and (ii) but aren't quite RPGs. Still, I think (i) and (ii) get most of it.
Most of the debate about whether or not 4e is a RPG turn on whether or not it satisfies (i) - although that is not always clearly expressed. To me it's obvious that it does - see, for instance, this part of the rules for damaging objects from the DMG (p 66):
Some unusual materials might be particularly resistant to some or all kinds of damage. In addition, you might rule that some kinds of damage are particularly effective against certain objects and grant the object vulnerability to that damage type. For example, a gauzy curtain or a pile of dry papers might have vulnerability 5 to fire because any spark is likely to destroy it.
The fiction - ie
here is a pile of dry papers affects the resolution -
additional fire damage is applied to the objects in question.
Similarly, the DMG and DMG2 discussions of skill challenges talk about the role of the GM in framing each check, adjudicating, adjusting the fiction appropriately, and then re-framing for the next check.
My (purely anecdotal) observation is that many if not most of those who complained about 4e not being a RPG also ignored these parts of the rules about making fiction matter to resolution.