It wasn't a miscommunication. The pilot understood and was attempting to correctly follow the instructions of ATC. The error (as far as we can tell) was that the pilot wrongly believed that they were following those instructions, but the pilot did not know where they were.

So the next logical question is 'why didn't the pilot know where they were?', and there are a lot of possible answers to that question, which could conceivably be linked to communication (e.g.: not enough signage, they were told incorrectly, their maps were written in Klingon), but the primary problem was that the pilot believed they were crossing a different runway to the one they were actually crossing.