I don't know if she's the best out of everyone at the entire competition (see Katie Ledecky, Michael Phelps, Kim Rhode), but she's absolutely the best in her sport, and probably the best gymnast ever. There are a lot of amazing athletes and not all of their accomplishments are gold medals. However, in the gym, she's a shining star.
She has proven her worth as a athletes in one of the most difficult Olympic events. This definatley makes her the best athlete in the Olympics this year, and quite possibly ever. There is no one better than her. SHe is without a doubt an exceptional, world class athlete and has no true rival.
It is impossible to judge whether Simone Biles is the number-one, absolute best athlete at the Rio Olympics. If the 'best' is measured in the number of gold medals won, she did not win as many as some other athletes, so she wouldn't be the best. If the 'best' athlete is measured by the athlete with the absolute highest scores, she would be a contender but probably still not the absolute best. There is no way to single out one athlete in a competition with so many different sports as the best.
Biles may be the best gymnast, or even the best all-round female athlete at the games. Phelps and Kenny, however, excel at a number of disciplines within their sport (like Biles) but also have a number of medals from previous games that prove their sustained and continued pedigree when compared to Biles.