This one needs very little adaptation to work over video chat. Most people have five six-sided dice somewhere in their home, right? Just rummage through other games you have at home.
To play remote, everyone will need five dice, a cup, and a notepad. If you want to make it all official-like, you can each print out Yahtzee scorecards. Otherwise, you just play as normal. Everyone takes turns rolling their dice, finding the best-scoring combinations of their roll, and recording them on their sheet. You should roll within view of the camera though, to discourage cheating.