The meaning of the idiom, to play dumb, is to pretend not to know or understand.

...is obviously known to the authors of the original text but not to those who offered their guesses as translations here
Indeed, anyone who saw M. Prokhorov earlier this week would hardly perceive his behavior as "playing dumb," "having nothing to do with it" (did you wonder what is the 'it' here?), or going "loose / over the board" (whatever that means)
Some guesses in the discussion are even wilder: do you really see him as withdrawn (<-> замыкаться), embarrassed (<-> стесняться), or trying to get himself out of the mess (<~> предпринимает конкретные действия, чтобы не оказаться замешанным...) after he's just declared war against Surkov?! That sounds... excuse me, can't find a good printable word here :)
The unexplained ones aside, let's look at the association with "отморозок" as the only one so far that looks not so clueless
Yes, "hell-raiser" sounds more like Prokhorov's image these days -- see
http://www.thefreedictionary.com/hell-raiser
But, to be precise, the meaning of "отморозок" most widely used in the media and spoken language is
"человек, полностью лишённый нравственных принципов (a totally immoral person); негодяй ([any synonym of] scoundrel)"
http://ru.wiktionary.org/wiki/отморозок
Those who believe it rings the right bell with regard to Mr. Prokhorov's behavior should stop reading right here
Those who don't may want to go etymological and look at the origin of "отморозок" in Russian criminal jargon

These definitions can be found on the page linked at the bottom:
- отморозок = отмороженный (synonyms: фраер без понятий, дикий фраер) = не признающий воровских законов, живущий не по понятиям (disrespectful of, or living against, the laws of criminal world)
- понятия = негласные воровские законы (unspoken laws of criminal world); правила, нарушения которых порой грозит виновнику смертью или большим штрафом (rules such that one who breaks them may be condemned to death or a large fine)
By the way, note that
- фраер = гражданский человек (anyone who is neither a criminal nor a policeman/prosecutor/jailer/...)
and it's important for understanding the present context that "дикий фраер" is an antonym of
- честный фраер = персона, придерживающаяся законов, правил и договоренностей (a person who adheres to laws, rules and agreements)
In the same glossary,
- отмороженный на всю голову = психически неуравновешенный (deranged); беспредельщик
where 'беспредельщик' derives from
- беспредельничать, беспределить = нарушать воровские законы, понятия или договоренности (to break -- more literally, to go beyond the limits imposed by -- laws, rules or agreements that must be observed in criminal world)
On the one hand, anyone familiar with Russian criminal traditions knows that disrespect of "понятия" was regarded by those "loyal to traditions" as a kind of insanity
On the other, the connotation of "отмороженный" as deranged explains the transformation of "отморозок" into its meaning in Wiktionary

Now 'отмораживается' should make perfect sense if you've heard "по понятиям" as applied to the unspoken laws of present-day Russian politics
Still unsure?
Read another definition:
разморозить зону = поднять зэков на бунт (to stage a prison riot)
There is a wider subtext connecting this one to all given above: 'замороженный' (frozen), as antonymous to 'отмороженный,' refers both persons and situations complying with unspoken rules
Speaking of situations, such rules are supposed to be observed not only by prison inmates. When jailers fail their part, there comes a call to "unfreeze the zone"...
Compare this with "еще немного — и на баррикады" -- and you may find a correct English equivalent for 'отмораживается' in the context

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Note added at 19 час (2011-09-17 18:38:18 GMT)
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Correction:
refers -> refers to
Sorry about the typo

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Note added at 2 дн20 час (2011-09-19 19:00:14 GMT)
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Indeed, 'warming up' may sound related to 'разморозить зону' (if a riot is viewed as a kind of "energetic action") but not to 'отмораживается'
The key to understanding is the opposition between
'замороженный' (literally, 'frozen') ~ loyal to unspoken rules (see above)
and
'отмороженный' ('unfrozen') ~ refusing to follow the rules
Accordingly, 'отмораживается' (literally, 'is changing from frozen to unfrozen') refers to one who begins to disobey defiantly
That is,
"the dude is flouting the unspoken laws"
would be a much closer equivalent of
"отмораживается чувак"


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Note added at 2 дн20 час (2011-09-19 19:02:13 GMT)
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I mean, 'flouting' is much closer in meaning to 'отмораживается' than 'hell-raiser'