A strict reading of the text - that is, if the grammar is correct and consistent - tells us that in this scenario, Earth suffered some extinctions, including humans, but is not lifeless.
Earth is the only planet with life in the milky way.
Since this is present tense, we know that Earth still has life at the time of the writing.
The most progressive life form of which were the Humans...
Since we are using the past tense "were", we know that humans are no longer a life form of Earth.
[Humans] who ... brought about extinction on the blue planet.
At least some extinctions were caused by Humans.
However, it is important to take the context of the writing into consideration. The minor errors on the source page (e.g., the extra comma in "It is this life form, that is responsible for the damage to the existence of life.") tell us that the author may not be 100% accurate with grammar. The author is also clearly concerned with human impact on the environment: "Yes, it's us, the mighty bipedal animals that rule this kingdom, and slowly dragging it to ruin."
Based on the context, I believe the author's intention with this text was to say "Earth was the only planet with life in the Milky Way." This is more consistent with the repeated warnings on the authors page, and also a better-written scenario.
(I am still curious where the alien writing about Earth is from, since we know Earth was the only planet in our Galaxy with life!)