The legal criticism would be that there just aren't that many unique melodies—as demonstrated by the fact that they were able to enumerate them all—so the mere fact that two songs use the same melody is not sufficient to show that one is a copy of the other. The set of melodies that are compatible with human ascetics is even smaller. They don't actually need these auto-generated melodies to qualify for copyright for the project to succeed. It works equally well if similarity in melody is not considered sufficient evidence of copyright infringement.
Even just having the database around so that one can say that they copied the melody from here rather than from some other source might be enough. After all, unlike patents, independently producing something similar to a copyrighted work is not infringement; you have to have actually copied from the other work. If you're a musician perhaps you should listen to a few randomly-selected melodies from this program each day. Maybe it will spark something, but even if it doesn't it will at least make it harder to argue that whatever melody you come up with could only have been "subconsciously copied" from some other composer's song you may have heard decades ago.
How does that follow? You can enumerate any finite number. And the article doesn't say how big. Is it a thousand or a trillion? "Riehl says the algorithm works at a rate of 300,000 melodies per second.". The article doesn't say how many seconds it took to generate all melodies though.
Not within a fixed time period in the real world. You're limited by the matter and energy available, and by the speed of light. However we're not talking about the theoretical ideal limits of computation. The upper bound would be 300k melodies for each second since the program was written—68.7 billion in all, according to the Adam Neely interview linked from the Press page of the project site. Which is a lot, but then there are hundreds of millions of known songs, each of which is likely to contain multiple melodies, some of which are much more likely to be chosen than others. Accidental duplication is thus quite likely.
In some sense, looking at information as being exclusionary and as being inclusive are the same thing, but there's a lot of ways in which the former actually makes more sense as a thought framework.
And in this particular context we can see how that plays out... a list of all possible melodies of a given nature actually has very little information in it, because it doesn't exclude enough. It may superficially seem to our human senses that a lot of stuff has been included/constructed, but in reality, the 'list of every possible melody' is a vapor. There's not actually anything there. It is the act of exclusion of possibilities that leads to interesting information. Such information as this list has is contained in its specification of what a "melody" is. Counterintuitively (to a lot of people's understanding), if they widened the specifications, while they would end up with a bigger list they'd end up with less information in the result.
The act of creating a song isn't a matter of creating the possibilities from the raw nothingness, it's a matter of carving them out of the exponentially-large space of possibilities and finding something there useful. The exponentially-large space is so large that it is very easy to not see it that way, because, I mean, it's huge. It doesn't feel like "removing" possibilities the way carving a 3D stone does ("I remove everything that doesn't look like my desired statue"), because the exponential space is so inexpressibly larger, and we need fundamentally different tools to address such a space, but in the end, it's the same thing.
While this isn't what the law was written for necessarily, the "creativity" requirement here could be very easily pressed into service here. They've expressed very little creativity/exclusion on this list and it would be easy to argue it falls far below the threshold necessary for copyright. As a literary criticism of the system, it is successful and thought provoking... as a legal criticism of the system it would fail completely.