Idea for a Birthday Gift. (N) Dota Expert

If you're not sure, I guess a bunch of Treasure Keys would always be appreciated - although that's almost similar to giving a gift voucher instead of the gift itself, so I'm not sure if you'd want that.

Buy him lots of crates that don't require keys :)

I would check his most played heroes first, and see what items he already has, you could get some nice item sets for that (some arcana maybe, though they rised the price lately I think)
http://www.dotabuff.com/ You can try checking his stats there if he enabled public stats, otherwise you would have to install dota and check his profile through client.
Or try to ask him who he likes the most, saves the trouble, you could pretend to be interested in the game or something to keep it secret. Hope that helps a little.
edit: Once you know the hero you can go to http://dota2.gamepedia.com/Equipment to easily browse through the items/sets and pick something.

..You really need to ask what heroes he likes. Buying something then discovering he doesn't play the respective hero isn't really a good option. There ain't a lot of things in dota that can be equipped by more than one character; I imagine some runes,wards and couriers can be okay,but wards are used almost exclusively by support-type characters,and non-hero-specific runes cost cents. There are a LOT of couriers and a lot of effects and it really just comes down to his choice(buying something in that range and discovering he doesn't like it is bad).

If you don't want to ask him what heroes he likes,it may be possible to discover that if he has public match history on and you comment with a link to his profile.

Buy him The Demon Eater (I have no idea what it is, probably some set).

Edit: It's an Arcana.

Buy his favorite hero equips on dota 2 worth 25$ or buy him Arcana Items (which is most expensive items in dota 2).

Having used the magic of looking at your friends list on Steam and checking Dotabuff, I have determined that your friend's most played hero overall is Rubick and his most played hero recently is Lich. He already has a few Rubick sets, so instead, I recommend the Dead Winter set for Lich:

Dead Winter Soul (MAKE SURE YOU GET ONE WITH THE DEADWINTER'S SOUL KINETIC GEM SOCKETED, NOT AN EMPTY SOCKET): http://steamcommunity.com/market/listings/570/Dead%20Winter%20Soul
Dead Winter Mantle: http://steamcommunity.com/market/listings/570/Dead%20Winter%20Mantle
Dead Winter Sash: http://steamcommunity.com/market/listings/570/Dead%20Winter%20Sash
Dead Winter Grasp: http://steamcommunity.com/market/listings/570/Dead%20Winter%20Grasp

Of course, that's well under budget, so you could also going get your friend an Unusual Courier. I can't really provide a single link here, beyond the market page for unusual couriers ( http://steamcommunity.com/market/search?q=&category_570_Hero%5B%5D=any&category_570_Slot%5B%5D=any&category_570_Type%5B%5D=any&category_570_Quality%5B%5D=tag_unusual&appid=570 ), but I will advise you 1) to look up the gem type and color on Youtube to get an impression of what it looks like and if your friend might like the effect, and 2) not to get him a Greevil because most unusual Greevils are actually common as dirt and those that aren't are hideously expensive

More on your friend's Dota-playing habits can be found on his Dotabuff page: http://www.dotabuff.com/players/11643746

EDIT: Huh. Unusual market link didn't work out too well. Try quoting this post, and copy-pasting from the quote.

i love the new Pudje Set....(Murder of Crows (Dendi's Pudge Set)) ONly 5,99E Love this!