1.此题答案错误,正确说法是：
It was in the 1984 Olympic Games that he won the medals.
2.此句为强调句型.其结构如下：
It is/was + 被强调部分 + that + 句子的未被强调部分.
该句型的最大特点是：去掉It is/was和that之后,剩下部分能构成完整的句子（有时需要调整句序）.
3.该句去掉It was和引导词that之后,句子剩余部分为：
He won the medals the 1984 Olympic Games.
很明显,此句在the 1984 Olympic Games前面缺少介词in(“在奥运会”的介词为in,不是on).
所以,此句必须在the 1984 Olympic Games前面加上in才能成立.
4.至于楼上说的:
It was the 1984 Olympic Games in which he won the medals.
或：It was the 1984 Olympic Games when he won the medals.
这两句话也是正确的.只不过它们采用了定语从句的语法.
其中：关系副词when = 介词in + 关系代词which = 介词in + 先行词the 1984 Olympic Games,在定语从句he won the medals的时间状语.
5.当然,It was the 1984 Olympic Games that he won the medals.这句话在口语中是可以成立的.
因为that在口语中可以代替关系副词when,引导定语从句,而且此that甚至可以省略.
但是这种语法现象一般不会出现在考试中.