The sniper example has been hand-crafted to specifically lead to the end result that was wished, by fine-tuning the probabilities just so.

The (Weak) Antrophic Principle makes no statement on probabilities, but only states that we of course live in an universe supporting life, because if it would not support life (or to be more exact, an observer), we could not be here.

So, TLDR, the one has nothing to do with the other.

To speak to your example again: it tunes the probabilities so the observed outcome was very, very unlikely, and also openly makes very clear statements about the actual probabilities, by saying something about 99% accuracy, describing the practice of the shooting and so on. From that it infers that there must be intent. And it is correct! There was some intent. Maybe all the shooters had secret orders to miss the target. This would be a very simple explanation, it would explain everything perfectly well, it would not require mystical reasons and so on and forth. Heck, one could even come up with valid reasons for this when writing a book or movie - maybe the whole operation was designed to scare the victim out of their mind, and play some awful mind game for whatever reason. Weirder stories have been written.

But this has nothing to do with the WAP. As mentioned, the WAP makes no assumption about probabilities of life, nor of whether slightly tweaking any of the universal constants make life impossible (maybe our style of life would be - but who says that other forms of life would not be possible), nor how many universes there might be (serially, one after each other, or multiverses). There are modern arguments (roughly following Darwinism) which explain very convincingly how the fundamental concepts of evolution do not only apply to fully formed life, but also to early states where non-biological chemicals form themselves to more complex structures and so on and forth (The Selfish Gene is a relatively old, but still fascinating read, and the current edition has many footnotes mentioning related, later works). So all in all it could perfectly well be that the probability for life in an universe, even with different universal constants, would be high. Again, the WAP does not require any statement about that. This is just to explain that the two arguments have little to do with each other.

More reading in the SEP, in the page on Fine-Tuning.

The Strong Antrophic Principle (which the question is not about) says that the universe was configured just so, to enable human life; i.e. it includes intent.

The Weak Antrophic Principle (WAP) does not include intent, and makes no statement on probabilities, but only states that we of course live in an universe supporting life, because if it would not support life (or to be more exact, an observer), we could not be here.

Your sniper example has been hand-crafted to specifically lead to the end result that was wished, by fine-tuning the probabilities just so.

So, TLDR, the one has nothing to do with the other.

To speak to your example again: it tunes the probabilities so the observed outcome was very, very unlikely, and also openly makes very clear statements about the actual probabilities, by saying something about 99% accuracy, describing the practice of the shooting and so on. From that it infers that there must be intent. And it is correct! There was some intent. Maybe all the shooters had secret orders to miss the target. This would be a very simple explanation, it would explain everything perfectly well, it would not require mystical reasons and so on and forth. Heck, one could even come up with valid reasons for this when writing a book or movie - maybe the whole operation was designed to scare the victim out of their mind, and play some awful mind game for whatever reason. Weirder stories have been written.

But this has nothing to do with the WAP. As mentioned, the WAP makes no assumption about probabilities of life, nor of whether slightly tweaking any of the universal constants make life impossible (maybe our style of life would be - but who says that other forms of life would not be possible), nor how many universes there might be (serially, one after each other, or multiverses). There are modern arguments (roughly following Darwinism) which explain very convincingly how the fundamental concepts of evolution do not only apply to fully formed life, but also to early states where non-biological chemicals form themselves to more complex structures and so on and forth (The Selfish Gene is a relatively old, but still fascinating read, and the current edition has many footnotes mentioning related, later works). So all in all it could perfectly well be that the probability for life in an universe, even with different universal constants, would be high. Again, the WAP does not require any statement about that. This is just to explain that the two arguments have little to do with each other.

More reading in the SEP, in the page on Fine-Tuning.