Are gametes determined by the sex of an organism?
The gametes produced by an organism are determined by the organism's sex - Thus, that statement from Wikipedia appears correct to me. In the case of humans, males have two different sex chromosomes. Thus, males produce gametes with either a Y-chromosome or an X-chromosome (XY). Female humans also have two sex chromosomes, but they are two different X chromosomes (XX). Thus, when females produce gametes they have a single copy of one of the X chromosomes in each gamete. In most cases, a fertilized embryo results and is either XX or XY - in the case of males the embryo gets the Y from Dad and the other sex chromosome is one of the two X's from Mom. In the case of a female the embryo gets the X chromosome from Dad and one of the two X's from Mom. 



Here is an image describing what I said above with a link to the page to read more:



Here is a link from a basic genetics course from Dr. Young in the UK that has a more in-depth explanation. 

Here is a link to another article from Nature Education that help explain how this works in humans as well as some other organisms that are slightly different.