I disagree. The current text that you quoted says that a long rest is "a period of extended downtime, at least 8 hours long, during which a character sleeps or performs light activity". So benefiting from a long rest requires at least 8 hours of downtime, and downtime is defined as sleep or light activity. Time spent adventuring isn't sleep or light activity, and thus can't count towards the required 8 hours of downtime.
In your example, the total downtime is only six hours and 1 minute, and thus fails to qualify as a long rest. To work your example would need to be rewritten to look something like:
Sleep for 3 hours, Adventure for 59 minutes, Sleep for 3 hours, Light Activity (or Sleep) for 2 hours.
Then the total amount of downtime would satisfy the eight hour minimum.