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I appear to have encountered a position in which it is impossible to logically determine whether or not a square is a mine. From the research I have done, it appears that
a) A unique solution and
b) A method to determine this solution without any guesses
are central rules of this game.

Here is a screenshot of the final position: enter image description here

The bottom right 4 squares require a pattern of two squares with mines, and two without, forming the diagonals of the square. Basic logic shows that that is the only way to solve it. In the top section of the square, exactly 1 mine must be filled, so that rule of the square with a three is not broken. If you fill two, then the rule of the 3 square is broken. Likewise, at least one of the bottom must be filled, in order to fill the required amount of mines. The two mines cannot be adjacent to each other for the following reason:

Case 1) They are both in the left column of the square.
Then, the rule of the 2 square is broken (too many mines)

Case 2) They are both in the right column of the square.
The rule of the 2 square is again broken (too little mines)

The question is whether or not I am correct in saying that this is a non-unique solution.

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There is no contradiction here. The base rules of Minesweeper just state that there are mines, and that the number of mines adjacent to any square is indicated. A guarantee of uniqueness or logical deductibility is not required.

Any variation on those rules is solely an implementation choice.

While some implementations do guarantee a logically unique solution, Microsoft's implementation of Minesweeper does not. This isn't against the rules of Minesweeper - it's just a decision the developers made, like automatically clearing empty spaces. While it is frequently possible to make an educated guess based on likelihoods, the game makes no guarantee that logic alone will lead to a solution, and it frequently does not.

Some situations will always split 50/50, like this one.

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You seem to confuse Minesweeper the well-known puzzle computer game with the derived Minesweeper pencil puzzle type. As others have answered, the former does not guarantee a unique solution. The latter starts out with a grid where some minesweeper clues are given, and the location of all mines can be uniquely deduced from the givens.

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