"Man has the ability to speak."
Translation:De mens heeft het vermogen om te spreken.
If the sentence doesn't change meaning at all, "Om" can or even has to be left out. http://taaladvies.net/taal/advies/vraag/597/om_hij_ging_weg_niet_meer_terug_te_komen/
"Om" is indeed optional here. However, it is different from the examples given in your link, where "om" has the meaning of "vervolgens" or "waarna". In Dutch the phrase "het vermogen om te ... " is commonly used and perfectly acceptable.