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Does anything in copyright law entitle Apple to impose conditions on the use of software it gives away for free online (e.g., that it may be run only on Apple hardware)?No. Nothing in copyright law allows this. However, everything in contract law allows this.
Copyright law forms the underlying background situation only. Under 17 U.S.C. § 106, the default is that only the copyright owner may make copies (including, e.g., the copy made when installing the software or the copy made into memory when running it).
However, those exclusive rights may be licensed to others. (Under 17 U.S.C. § 117, a software licensee, or the lawful owner of a copy of the software, may always copy the software to install/run or to make an archival copy.)
Licenses are governed by contract law. Contract law typically consists of an offer, acceptance, and some thing of value traded by each side. Restatement (Second) of Contracts, § 17(1).
The thing exchanged can be a promise, a forbearance (i.e., a license), a conditional promise, or any number of things. Restatement (Second) of Contracts, §§ 71-81.
In this case, the license to copy the software to your internal storage and from there into RAM is offered conditionally. In return, you promise not to run it on non-Apple systems. If you break your promise, the conditions of Apple's license to you are triggered and your license terminates. All of that is governed by contract law.
The backstop to that, though - the legal stick - is that now you're using an unlicensed copy and continuously copying it into RAM to use it. That is what opens you up to copyright violation liability.