How is it possible that a German withholding tax is levied on a dividend payment of an ETF, while the ETF is located in Luxembourg and is listed on an Irish Stock Exchange?

The tax treatment differs per Exchange Traded Fund (ETF) and is among others dependent on the fund structure. The following aspects need to be considered:

A fund can be considered fiscally transparent or non-transparent. Income received through a fiscally transparent fund is considered to be directly attributable to the participant of the fund (for tax purposes you have to look through the fund). In case of a non-transparent fund, the income flows to the fund itself.
Whether a fund can be considered fiscally transparent is dependent on the local legislation in the country where the fund is established. This may differ per country.
To answer the question asked; German withholding tax can be levied in the case that the ETF is considered a fiscal transparent fund based on Luxembourg legislation and the income the fund receives originates from a German investment. The income and the accompanying German withholding tax are then attributed to the fund participant who is considered to have received the income directly.