Your version isn't wrong at all. It's correct to say 'A firm has a competitive advantage when it implements a strategy THAT competitors are unable to duplicate or find too costly to try to imitate'. We can write this sentence with or without the word 'that'. Both forms are correct. You can choose - it's up to you whether you use the relative pronoun or omit it. If using 'that' makes it clearer, either for you or for your reader, that's fine - go ahead and use it!
And yes, there is a rule. Here it is:
The relative pronoun is optional if it refers to the OBJECT of the sentence, in this case 'a strategy' .
The relative pronoun must be used if it refers to the SUBJECT of the sentence.
For example, take a look at the following sentence, which actually contains two relative clauses using 'that'. In both instances, the relative pronoun has to be used because it refers to 'the companies'. 'The companies' is the subject of the sentence, so you have to use 'that' - the same as you would in Italian.
The companies that have a competitive advantage are the ones that implement innovative strategies.
I hope that helps.