[samirm]

are chess players required to write down their moves?

or could the event organizers set up some overhead cameras

or make a smart board

and automate the entire thing that way?

[yesenadam → samirm]

>are chess players required to write down their moves?

Not at fast time controls, or with little time left.

"If a player has less than five minutes left on his clock at some stage in a period and does not have additional time of 30 seconds or more added with each move, then for the remainder of the period he is not obliged to [record moves]." http://www.fide.com/FIDE/handbook/LawsOfChess.pdf

And smart boards are expensive.

[samcal → samirm]

The answer is yes to all 3! There are cameras and smart boards at the highest level, but chess players are still required to write down their moves. Archaic for sure, but tradition is strong with these old games.

[indy7500 → samirm]

Yes that's all possible, just a lot more expensive.