I bought it the day it was released.the day 前面是否省略了介词？

是。

原本应该说：I bought it on(或during) the day it was released.

I bought it on the day when it was released. 这样累赘的表达很有问题。

I bought it the day it released 就正确了

没有省略

给你些例子吧：
I'm OK today!
You were not here yeterday.
He couldnot work that day.
这些句子中，表示时间的词都没有介词。
这样你该看出来了吧

It's grammartically correct.