I don't get it. I've been playing theater of the mind since I started playing D&D. I have never experienced any arguments about anything involving positioning and movement.
Just to be clear - you're saying that, in a context in which everything is worked out simply by description, you can't imagine someone being unclear about whether a particular PC is 5' or 10' from a particular enemy, or a particular pillar?
I can say that I've frequently had this issue, and have resolved it either by using a grid and token (pretty standard in my 4e game unless the layout is very simple) or by drawing a quick sketch map.
Here's an example, in dialogue form, of how uncertainty can arise:
GM: You are at the entrance to a large hall, 70' long and 30' wide, with two rows of pillars dividing the width of the room into thirds. The pillars are about 10' apart. A group of goblins - a dozen or so - is gathered at the rear of the hall.
Player: I move into the room as far as I can, but staying out of reach of the goblins, and take cover behind one of the left-hand pillars.
From that description, how many of the dozen or so goblins can see the character without moving? Against how many does the PC have half or 3/4 cover? How many pillars are between the PC and the entrance? Between the PC and the nearest goblin? Between the PC and the furthest goblin?
The description does not provide enough information to answer any of those questions. That is the "vagueness and nebulousness" that the reviewer is referring to. The potential for arguments arises when the player starts debating with the GM exactly how many goblins his/her PC has cover from.
An argument is most likely to occur if the player believed that his/her action declaration satisfied both these descriptions - (i) my PC has moved as far into the room as s/he can while staying out of reach of the goblins, and (ii) my PC has cover from all the goblins - while the GM believes that, precisely
because (i) is true, so (ii) must be false. The GM might reach this belief because s/he is envisaging the leftmost (from the PC's perspective) of the dozen-odd goblins actually has a clear line of fire to the PC hiding behind the left-hand pillar; or because s/he is envisaging the PC hiding directly behind the pillar (rather than to its left) and hence being exposed on her right flank to a goblin who is on the right side (from the PC's perspective) of the group of goblins.
There are ways of avoiding such arguments, of course. One is that the player just acquiesces to the GM's ruling. But that reduces immersion and player agency, as the player has in effect been led into a choice which makes no sense from his/her PC's point of view (because, after all, the PC could judge which goblins would have LoS to him/her, to what degree, by taking up a particular position behind a particular pillar).
Another is to allow takebacks based on clarification between the GM and player as to what exactly the player was hoping to achieve, and what the GM's conception of the ingame situation is (eg the GM explains that, to establish cover against all the goblins the PC will have to stay closer to the entrance of the hall, rather than closing as far as the initial action declaration suggested). But takebacks can be clunky in play, they obviously slow things down, and for some players they are also problematic for immersion.
Another is to use an imagined visual depiction: the GM describes the scene with geometric precision (ie quite unlike my example above), and everyone remembers and acts upon that description in making and adjudicating action declaration. But this is not really "theatre of the mind" in any meaningful sense - it is to an actual grid as blindfold chess is to chess played on an actual board. Of course, often the GM will be using an actual visual depiction, but just not making it public - in which case the "theatre of the mind" is purely in the players' minds, but not in the mind of the GM, who has some external visual representation (eg markings on a dungeon map).
I'm guessing that the reviewer doesn't find any of the above-mentioned approaches satisfactory except perhaps for the last.
When I used to GM Rolemaster I would use a mixture of the second and the last approaches - ie allow takebacks/consensus to establish what was going on, and if the positioning was going to remain tricky I would draw a quick sketch-map, with a few markings to indicate distances if necessary, thereby clarifying who was where and what the options for movement were. (Rolemaster is more forgiving for this than 5e, I think, because it doesn't have OA rules: it uses a variety of other mechanics, not dependent upon positioning, that create incentives not to disengage from melee. So you don't have to keep track of who moves into and then out of the reach of whom, you only have to keep track of departure and arrival points. It can have the same issues with cover, however, as the reviewer complains about in 5e.)
