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It’s a similar reason structural concrete is so strong. They utilize a concept called prestressing. Keep in mind for the explanation that tension is the opposite of compression. If something has no forces acting on it, then it’s right between the both of them.
See, concrete is extremely weak in tension. You can practically pull it apart by hand. But how do we build bridges with it if it’s so weak? Well, we build them with rebar that is pulling extremely tight. Since the concrete is always being pulled in, it’s always in compression. Concrete may be a pushover in tension, but it’s incredibly strong in compression. So, we are always leveraging concrete’s natural strength by not allowing it in tension.
Prince Rupert’s drops do the same exact thing. The process of creating them makes them stupidly strong in compression in a similar way: The outside is already tight around the center when it’s first made and very hot, but then it cools down. It wants to shrink around the center but it cannot. That keeps everything in strong compression, so forces that would normally break it by pushing it into tension are absorbed, keeping the piece still overall in compression.
It’s also much easier to break if you hit it at an angle, as that causes a mix of tension and compression stresses. A hydraulic press is axially calibrated to be extremely straight, and essentially acts only in compression. This makes it perfect to show off the strength of Prince Rupert’s drops.
Side note, the tail is extremely weak! It’s a glass cannon, but the hydraulic press video shows off its absolute best-case scenario strength while hiding all of the weaknesses, like a well-engineered part!
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