From the link you provided from the IRS:

"You are not eligible for a payment if any of the following apply to you: You may be claimed as a dependent on another taxpayer’s return (for example, a child or student who may be claimed on a parent’s return or a dependent parent who may be claimed on an adult child’s return). You do not have a Social Security number that is valid for employment. You are a nonresident alien. The following are also not eligible: a deceased individual or an estate or trust."

That is exactly where I found the information for the first payment.  The IRS says if the person died before the first payment you have to return it, but the second payment was mandated that it could still go to a deceased person, so the second one does not have to be returned, but the first one does.