It mostly had to do with the weapon's overall versatility. As part of its default AA configuration, the 88 could depress below the horizontal, something its contemporaries like the American 90mm M1 could not do. This allowed the platform to be deployed as an ad-hoc anti-tank and field gun as necessary, which proved to be crucial when German forces suddenly faced heavily armored vehicles like the British Matilda that their dedicated anti tank guns could not face. It is important to remember that, as far as I know, prewar anti tank doctrine centered around lightweight guns capable of being maneuvered by groups of infantry, ie the 37mm platform. When vehicle armor proved capable of defeating those calibers, the only high-velocity solutions available were in AA weapons originally designed to engage high-altitude aircraft, and the 88 fortuitously had that dual-capability designed into it from the outset. The gun also benefited from the German tactical situation of being largely on the defensive, negating its disadvantages of lack of mobility and emphasizing the gun's range and high velocity. By contrast, the mobile-conscious and offensive Allied forces had fewer opportunities and different doctrine to employ heavy anti-tank weapons. It should also be noted that while the Germans were the first to use modified anti aircraft guns, they weren't the only ones. Notably the United States also set to adapting their 90mm weapon to the anti tank role after running into issues with German armor, though the American supply system was configured differently from the German model. The fact that the 88mm weapon was so widely proliferated also lent to its notorious reputation among GI's who brought their stories back home after the war was over.

TL;DR: It was deployed a lot, large-caliber high-velocity shells turned out to be more important than originally predicted, it had a wider range of motion relative to its contemporaries, the Germans had more opportunities to use the platform to its advantages relative to the Allies, and it was seen a lot by its intended victims.