What does "Do you haz teh codez?" mean?
Solution 1:
Literal translation is "Do you have the code?" but what is implied is "Please can you write my application for me?" or "Please solve my problem so I don't have to put any effort in."
It is written like that as a mockery of people who ask questions on Stack Overflow, and other such websites, where their question is a thinly veiled, or completely unveiled, attempt to get someone to do their work for them. So the questioner won't have even have tried to solve their problem and will possibly be asking for an entire software application to be written.
I'm not sure what you mean by "Is there like a word game?" If you mean is this like a word game then not really, it's just a joke.
It should be pronounced "Do you haz (as in Mazda) teh (as in meh) codes?" and in IPA: /duːjuːhæztɛkəʊdz/.
For an example of the type of thing this is mocking: http://thedailywtf.com/Articles/plz-email-me-teh-codez.aspx
Solution 2:
So, to break it down:
haz=have teh=the codez=codes
So it means Do you have the codes? or in a bit more sensible form considering the context Are you able to code? (Code here meaning to write code, or program)
These are variations from internet memes (google lolcats, if you dare) that have become mainstream (usually in a tongue-in-cheek way). I'll stress this is NOT standard English.
Presumably the banner is done that way to catch someone's attention by avoiding a more standard (and therefore less engaging) phrase. It also may indicate that they're more tied into to internet/programming culture which has a history of using intentionally obfuscated terms/spellings/etc. to set them apart and to act as a shibboleth.
As for the pronunciation, you can pretty much just read it phonetically, as the alterations are intended to be applied to the pronunciation as much as the spelling.
Solution 3:
Sure, it means "do you have the code" ie.
"are you capable of writing quality code (ie, since it's a career ad you're reading, are you a programmer looking for work) and are you geek enough (since it's an ad you're reading, in the positive sense of the word, of course) to understand and like geekish talk like this (which implies that you'd fit a similarly geek company of computer experts well)?"
They write it like that because it's supposed to be cool and to match the target audience's usage.
As for a word game being there - no, there's none imo, apart from the above.
For the pronunciation, go here and click listen. ;) (That's half a joke, sure. But I'm fairly sure the majority of... errr... geeks would get and like it.)