Do Dutch speakers actually differentiate between t and d sounds at the end of words? The d at the end of gegooid here sounded distinctly like a t to me.
You noticed correctly. In Dutch, we do not differentiate between t and d sounds at the end of words: it is always pronounced as a t. This has got to do with the difference between voiced (such as a d) and voiceless (such as a t) consonants. Dutch devoices all hard consonants at the end of words.
For more information, see: https://en.wikipedia.org/wiki/Dutch_phonology#Final_devoicing_and_assimilation