Q: Is it permissible to pray tarawih prayers at home behind a live streaming internet prayer?
No. It is not permissible to do pray behind an imam who is in another place while following them through the internet or TV. One of the conditions of praying in congregation is that the imam and the congregants are in the same space. This would not be the case when praying behind an imam by following through a live stream and as such the prayer would not be acceptable.
However, it should be mentioned that it is permissible to pray tarawih at home by oneself. This was even the practice of the Prophet (pbuh) because he did not want people to think that the tarawih prayer in the mosque is required. It is preferable that the person prays in the mosque with the imam, but acceptable for one to pray at home as well. The person may also benefit from holding the mushaf and reading out of it directly while praying by themselves at home.
And God knows best.