Типа/наподобие/вроде govern Genitive, which in English can be rationalized through the question of
which/what type? or more literally
of the type of what? - of the type of that, also mind that in combination with
такого is a Genitive of
такОЕ and not of
такОЙ, and instead of
типа такого you can also say
такого типа where
такого refers to the
тип which translates as
of such type into English.
типа такой/ая/ое/ие (and in other inflexions required by the predicate) is also a valid combination, applicable in interrogative sentences where a speaker asks about a kind of something, but in this case
типа is a rather slangy filler word or a slang variant of the normal
вроде/наподобие + Genitive pretty low in register, e.g.
- (a punter) Мне нужен портфель such and such
- (a salesman showing a briefcase) Типа такой?
And as a follow up... Он типа такой крутой полицейский. -- This is
where the confusion comes in. Shouldn't this then be "типа такого"?
The chosen case conditions the meaning, in Nominative it expresses sarcasm, whereas in Genitive it's a straightforward expression of semblance to something with no hidden agenda. It could be that in the policeman sentence the case wasn't chosen very carefully if it meant to express just semblance. Admittedly in practice some overlap may occur in use of both cases but the first meaning i get reading the policeman sentence is sarcasm.