Question: Could there be a missing transmission in the audio recording?
While holding short, AEE seeks clarification on what they can expect. "Please confirm what expected?"
Tower: "only 2 minutes sir, traffic 2 miles from touchdown, I call you back after landing traffic for departure runway 8R."
Then AEE asks, "We can maintain runway heading for Aegean 4553?"
Tower confirms runway heading to FL310.
Either a transmission is then missing from the audio, or AEE took the initial departure information (heading and altitude) as a clearance to enter the runway and takeoff. This type of basic error would appear unlikely for an A320 pilot; probably (hopefully) there is a missing transmission in the audio.
In the recording, there was no transmission to line up and wait, or line after landing traffic, or any line up or enter the runway and there was no take off clearance.
Although afterwards, Tower says "I said after the landing traffic, you will enter on the runway ..."
If the Tower said that previously, it does not appear to have been included in this audio clip.
Great job on the video and audio. Thanks!