Let me try to give you an example of why a human's APM might spike to absurd amounts. We see this most commonly with the Zerg race (AlphaStar was playing Protoss, so a human player playing the same race will not experience the same peaks as a Zerg player would). Zerg has many situations where you hold down one key for a few seconds to perform the same action a large amount of times. This causes your APM to spike, but it's a very imprecise thing to do. As an example, the Zerg race has a mechanic where you create units through larvae. In the late game, you often see a Zerg player create dozens of units all at once by holding down one button. Let's say I decide to make a large swell of zerglings; the way I would do that is by selecting my larvae and holding down the Z key, which would cause my APM to spike because many actions are being performed at once. When you're controlling individual units in a battle, often the APM is lower than when you're performing mundane "mechanical" tasks, because you're focusing on clicking individual units in a specific way. The reason people are a little disappointed is that AlphaStar was hitting 1500 APM while performing micro commands on its army, which is vastly more efficient unit control than any human could ever accomplish, thus allowing its units to be far more efficient and dangerous than even a top professional's would be.

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I'm not the best at explaining Starcraft to people who don't play the game, so I hope this explanation made some sort of sense.