"The book that I thought was on my desk is gone".
=> 내 책상 위에 있는 줄 알았던 책이 없다 [없어졌다]. (structurally close)
=> 책상에 있는 줄 알았는데 책이 없다 [없어졌다]. (more natural in real life)
"내 책상에 있는 것 같은 책이 지나갔다" is not correct because:
1. 있는 것 같은 is not right for "that I thought...". It has the wrong tense (present); its past form 있는 것 같았던 can work, but still not as natural as 있는 줄 알았던.
2 지나갔다 means "pass by". It is not used for "gone" except when referring to time that has passed. For physical things 없어지다 and 사라지다 mean "disappear; go away", and the state of "gone" is 없다 (not there).