TRAFFIC
A brief glance at alexa (I know, I know...) shows the source breakdown of his traffic:
http://www.alexa.com/siteinfo/twicsy.com USA (17.5%), India (13.4%), Indonesia (11.3%), Japan (4.1%)
More interestingly, it lists some feeder pages, and there's one interesting one:
http://answers.yahoo.com/question/index?qid=20090722010355AA...
Which contains this answer:
"Bonus - This is an easy way to include pictures you have uploaded to Twitter in an easy and automated fashion. Go to http://twicsy.com and type in your twitter username. You will see all of the pictures you have uploaded through twitter. Now scroll to the right and click on the 'RSS' button. Now you can use this automatically updated link of your tiwtter pictures."
RSS FEEDS
So... since people can use twicsy to find all pictures on a certain hashtag topic ( http://twicsy.com/?search=%23cinderella ) or from a certain user ( http://twicsy.com/u/onedirection ), they can include these in their own sites as RSS feeds, thus contributing to his overall server traffic, but perhaps not actual visitors.
BANDWIDTH
He does not actually seem to host (all/any?) pictures himself (i.e. little bandwidth), but wraps twimg.com files in his own RSS tags, adding links to his site.
TRAFFIC 2
By the way, his assertion of 6MM visits a month is reflected in the quantcast numbers:
https://www.quantcast.com/twicsy.com#!traffic
DEMOGRAPHIC
Also, pretty interesting affinity sites and demographic (younger males, no kids, not wealthy, college educated, more than avg african american and hispanic visitors) with a strong affinity for O'Reilly Automotive (perhaps not very similar to the audience of this site, hence virtually unknown)
https://www.quantcast.com/twicsy.com#!demo
GEO
Geo findings of Alexa seem to agree with Alexa, though strangely enough, India is missing from the top countries. Quantcast claims only 56k unique cookies from India. Perhaps someone one is using his site and responsible for a lot of the Alexa 13.5% ?
https://www.quantcast.com/twicsy.com#!geo
MONEY MONEY MONEY
If my theory of above average RSS traffic is right, only he can tell, think he could make more money if he inserted some adverts into his RSS feed. Not sure how well this would go over with Twitter, since he's not doing (most of?) the image hosting.
I also get the feeling something is amiss. The Alexa and Quantcast numbers are significantly out of whack (13.4% of all traffic from India, yet only 56k unique visitors) strikes me as odd. He may be spending a bunch of money on servers whilst others save money on using them as a tool.
On a personal level I find the design very unattractive and out-of-date, which may prevent the site from becoming much of a destination and could be linked to the 60+% bounce rate. If I were him I would figure out what competitors do ( like twitpic, which according to compete is an actual competitor: https://siteanalytics.compete.com/twicsy.com/ ) and take it from there.
Access to actual analytics could provide more ideas for money-making (or -saving).