Yes, your rewrite is acceptable.

As for your confusion, it looks like you might have a case of DAMS (Definite Article Meaning Syndrome, a relatively common affliction that often affects English learners. It's chief symptom is confusion, generally caused by the erroneous belief that definite articles are only used for things previously referred to and specified in a narrative or conversation).

However, there are other uses of the definite article – ones that don't seem to get as much attention in ESL classes. For example, the word “the” can also be used:

• to refer to things that are unique (The Mona Lisa hangs in the Louvre.)
• to make a generalized reference to something (Bob plays the piano.)
• with adjectives, to refer to a group of people (This is another tax break for the rich.)
• to indicate that there is enough of something (She will bake a pie, if she has the ingredients.)

In the passage you quote, the author elected to use the definite article to make a generalized reference to the flora and fauna of Africa: grassy woodlands, lions and tigers. The wording would only seem strange to someone afflicted with DAMS.

This is worth mentioning, too; under its entry for the, NOAD lists:

used with a singular noun to indicate that it represents a whole species or class : they placed the African elephant on their endangered list.

(Disclaimer: DAMS is an acronym I just made up for the purpose of this answer. It was intended to be humorous. However, this isn't the first time I've witnessed this confusion; I've encountered it several times on both ELL and ELU.)

I have considered that you have gone through this document here, the original source of this question and the other answer here, but then it's still perplexing.

So now...

I shall try to address the Or could you possibly explain that with another example that is easier to understand? part here:

Articles are difficult to understand and depending on the context their usage changes. I have recently asked a question on this.

Now, please note that I'm creating the context here.

The scene is — you are standing in the Sasan Gir Forest (home to the Asiatic Lions) and I'm with you providing some information about the area and the animals found in. I'll use all those three sentence structures in concern.

1: A lion is friendly

This means there is a (one) lion somewhere who is friendly.

What that explanation says -- "the extinction happens to every member of that species." Correct! Compare it with this example. Any one tiger cannot be in danger to become extinct. And yes, species is a group noun and can take indefinite article. OALD example says -"a rare species of beetle."

Now,

2: The lions are friendly

This in this context means I'm talking about the specific lions, precisely I'm talking about the Asiatic Lions who are friendly and not the African lions.

What that explanation says --"the predicate is the characteristics of the species." True again! However, in my example, I'm not talking about extinction but friendliness and hence, it could be understood that I refer to the character of friendliness of particular lions. When we are talking about extinction, we should expect this to be true of any tiger because when the species of some animal gets extincted, you don't find that animal anymore.

And finally,

3: Lions are friendly

This takes the entire species of this animal. It talks about the characteristic of an animal. As we say dogs are loyal, which means take any dog, it's loyal because it's it character.

What that explanation says -- "we are talking about the tigers in aggregate." Correct! This matches with the example given above #3. Without any article, it means you are talking about the entire mass, species as a whole. Check - dogs are loyal to humans.

All in all, the plural generic seems to be easily understandable for English learners like me.
This site confirms it! :)