Yes and no. It's not on their side as far as DDoS goes. They can only work to mitigate it, but it's not possible to completely deal with it, true.
However, it's entirely based on contract and law in whatever country the occurrence takes place. A paid service, if interrupted, may be obligated to compensate the person by it. For example, if your network won't work for 15 out of 30 days because a hurricane destroyed the cables, you don't need to pay for the 15 days that you did not have the network, and thus your monthly bill would be reduced by half. Well, in some countries.
Basically, you pay only for the days when you CAN make use of the service without interruptions (whether or not you actually do is irrelevant here), with the exception of times that are contractually void of service (like, in this case, maintenance). Unforeseen circumstances cannot be contracted.
The company in question could, of course, try for recompense of their own if the "unforeseen circumstances" were caused by another person, or they could try to get a dotation from the country if it was a natural calamity, but that is another thing entirely.
As I said, it is dependent both of the actual contract and law, and those vary from place to place. In practice, most people wouldn't (and honestly...shouldn't) even bother with smaller or larger interruptions. The likelihood of being reimbursed is pretty low, really. I mean, law enforcers aren't very well known for understanding that what is "small" to them may be majority of the "free" budget of the person in question, and being "objective" is a myth as far as courts go. Besides, one would probably lose much more money on the random costs like transportation than get from the favorable outcome of a case (if it was favorable in the first place).
However, theory is one and practice is another. You said that Square Enix doesn't "own" anything. That's a theory. And it is possibly incorrect. It may very well owe to some of the player base, but not to others.
Well, in case that it's the ISP's issue entirely...Square Enix have nothing to do with it, however. The ISP may be liable instead.