As far as I know, there's no evidence that he "acted out scenes from Cyrus' conquests." I'm pretty sure he wasn't obsessed with him, either. He was known to be an avid reader, however, and likely read Xenophon's Education of Cyrus (which was mostly fiction and hero-worship). The Greeks considered Cyrus Great to have been a very respectable leader. Alexander would have known conquering the Persian territories would require political finesse a la Cyrus, so he likely borrowed a lot of what he thought Cyrus' policies were.

He was known to be lenient toward people who surrendered to him without a fight, but absolutely brutal toward people who stood against him. He was seen as a liberator from tyranny in some cases, such as when he conquered Egypt. Cyrus portrayed himself in a similar way when he conquered Babylon, and a lot of his subjects definitely bought his propaganda. You can actually see evidence for this in the Bible.

After Cyrus began to solidify his empire he began adopting stylistic and cultural elements of his various peoples and incorporated them into his official regalia. Alexander did a similar thing when he conquered, no matter where. He adopted Egyptian religious elements, Persian court regalia and wives, and even commanded his generals and officers to do the same.

In essence this obsession you read about is probably just artistic license, but Alexander definitely thought about Cyrus' policies and strove to emulate them to an extent. That's not necessarily due to admiration, however, it could have just been Alexander's characteristic pragmatism.