As far as I know the Vanguard Global Stock Index Fund he uses accumulates instead of paying a dividend?
Buying shares of an index fund is the same as buying shares of every single company in the index, albeit much simpler. If there is a company in the index that pays a dividend, you'll receive it.
But a larger point should be made that there's basically no difference between receiving a dividend or selling shares to meet your income needs. The stock price drops by the dividend payout amount on that date.
If you have stock worth $100 and it pays a $5 dividend, then you now have $95 worth of stock and $5 in your pocket.
If you have stock worth $100 but it pays no dividend, you sell $5 worth and you have $95 worth of stock and $5 in your pocket.