They estimated that about 200,000 people attended the demonstration.
If there were EXACTLY 200,000 people the "about" was not necessary. In this case it is.
when we use "estimated" the preposition "about" is implied in it.
Richard is correct. If there were exactly 200,000 than it would not be an estimate which, by definition, is an approximattion, thus not exact.
an estimate is approximate; this is therefore a tautology.
You estimate a number. No need for 'about' here as it is inferred that it is an approximate/ around not the exact number.