Ok, here is the complete up-to-date text on the long rest:
A Long Rest is a period of extended downtime, at least 8 hours long, during which a character sleeps or performs light activity: reading, talking, eating, or standing watch for no more than 2 hours. If the rest is interrupted by a period of strenuous activity—at least 1 hour of walking, fighting, casting spells, or similar adventuring activity—the characters must begin the rest again to gain any benefit from it.
We have established that, as per Jeremy Crawford’s clarification and the wording in the playtest, walking, fighting, and casting spells, are all part of the category “adventuring activity.” A long rest is a period of 8 hours during which you sleep for at least 6 hours and perform light activity for no more than 2. An interruption of an hour or longer of adventuring activity also forces you to restart the rest.
Now, let’s suppose a party of adventurers sleeps for 3 hours, wakes up and begins adventuring for 59 minutes, goes back to sleep for 3 more hours, wakes up and spends 1 minute reading. Has this party completed a long rest? Let’s check.
Has the period been at least 8 hours long? Yes.
Has it included at least 6 hours of sleep? Yes.
Has it included more than 2 hours of light activity? No.
Has it been interrupted by at least an hour of adventuring activity? No.
My conclusion would be that this adventuring party has indeed completed a long rest, as the RAW defines it.