I think it should be ‘had robbed him’ as it is in the past. Maybe ‘for’ sick pleasure.

I would say that generally "with furious anger" would be considered redundant; it would be more typical to just say "furiously." To make your verb tenses match, you could either pair "He looks at me..." with "I've robbed" if you're speaking in the present or "He looked at me" with "I had robbed" if you intend it to be in the past. There are a couple of more subtle issues if you want it to read like an edited book, but those are the two that I think are the most significant.

"Ideal" is positive, while "sick" is a negative adjective. The reader's mind doesn't go smoothly through the sentence. It might help to express why it's his ideal chance - his only opportunity, or his craving for revenge, for example. Is it clear in context whether you actually robbed him, or did he just look like you did? You might consider "He looked at me in fury as he realized I had robbed him of any chance for his sick pleasure."

It should be: like I had robbed him… I would add: like I had just robbed him