I take trying to answer this as a challenge (mostly for myself)! 😅 Okay, enough of that...
So, the first thing I would point out is that it depends on the context you're asking in.
I stumbled upon a specific interpretation of the term (queer platonic relationship) when it is used to refer to a same sex or gender people that live together and are so close that could be perceived from the outside as they are in a romantic relationship (when in fact, it is not true). This would assume nothing about their sexual or romantic preferences and the term queer is most likely used to express the deepness of such a connection (and the same sex or gender).
A more literal interpretation would be what @EmotionsListener explained; so it would be a type of a relationship among aromantic people, as a form of their "main" relationship. And here you get into muddy waters since it is not trivial, even for people that experience romantic attraction, to explain the difference between what's platonic and what's romantic. It is often taken as granted that people "just know". At the same time, the "universal rule" of "strict categories do not exist, they are just helpful sometimes" holds...
As for somebody that may be aromantic and from the way others describe this, I'd compare a platonic relationship to a very close friendship. Such a relationship is valuable and fulfilling; you understand each others' emotions, you share your feelings and experiences, you are able to listen to each other and sooth each other when needed. You are there for each other in everyday life; making it easier and more enjoyable. There is simply no desire to cuddle, kiss, have silly talks, <fill in any other cliche from a romantic movie>... 😅
It may be beneficial from a practical point of view to settle this bond legally if your country allows it. At the end of the day we live in a society where monoamorous relationships are valued.
As a closing remark, I haven't mentioned sex and (a)sexuality on purpose. I think it is difficult to draw the line and I felt like it is an unnecessary one too. I don't mind either way regardless of the motivation.