Он чем-нибудь отличается от стандартного русского языка?
You assumption is basically wrong. First of all, Kaliningrad Oblast is not that isolated. I'm talking not only about some obvious things like common media space which drastically reduces dialectal differences all over the world.
The thing is that nowadays in modern Russian there's no such thing like full-fledged dialects - with separate pronunciation norm, grammar and vocabulary. There are some differences, for example, people from Ural have a subtly different pronunciation norm which is very hard to mimic to a speaker from other parts of the country. The same is true about some other regions (not all of them).
But this is by no means close to the dialectal differences in, say, French, German or Italian. You are from Poland, I have (very little) knowledge of Polish and, as far as I understand, even in Poland there are some well established dialects, but, once again, there's no such thing in Russian.
So, basically, when we are talking about regional differences in modern Russian, in most cases we can speak about few regional-specific words (as @YellowSky) had already mentioned. It is claimed that there are such words in Kaliningrad. But these words are not about something crucial and are not used in an everyday life though.