It's a huge factor in my experience especially if it's an exact match. I'd go as far as saying that an exact match KW domain will at least halve the necessary other SEO work to hit the number 1 spot.
It must be exact match though - even a plural difference doesn't give this huge boost.
The other thing is a secondary effect - a ranking boost due to CTR. Searchers are more likely to click on a domain redshoes.com.au when they are searching for 'red shoes' especially as Google emboldens the KW.