h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

You've somewhat simplified how Deep Blue worked...

Yes, it did do lookahead - but it didn't just blindly calculate the responses to every possible response to every possible response to every possible response. It chose which moves to perform lookahead on, based on their probability of being good moves. It also had ways of determining when a situation was 'tricky', and so warranted more processor time, and a way of rationing the time available to it so it didn't get in time trouble.
It was also programmed to try and steer the game towards more combinatorial areas, where it could easily outperform the human mind, and away from the more stylistic areas, where it was at a disadvantage. Kasparov, of course, did just the opposite...
I'm not exactly clear what you mean by 'skill' or 'wit'. Deep Blue did everything human chess players do, including such nasty things as putting pressure on its opponents if they are in time trouble, It knew when to gamble, and when to play safe - one of the things it could calculate was how risky a certain move was. And, just like humans, it rote-memorized large pieces of opening theory.

You're also wrong about the motivation - chess has been studied for a long time because of three main reasons:
1) A lot of people said that chess was a mark of real intelligence, and as such computers would never be able to compete in it - there are a lot of embarrasing quotes from famous people on this matter.
2) The problem was 'hard' - it doesn't have any symmetry, you require a large amount of lookahead to win (top human players typically look ahead 15 moves or more, depending on the situation).
3) there was a good deal of chess theory around, from the value of pieces, to the importance of control of the centre, do the swathes of opening and endgame theory.

The maths of chess isn't particularly easy - certainly not compared to games like connect 4, backgammon and poker (where computers won a long long time ago). It gets nastily non-linear in places, certainly. Everything Deep Blue did may have just been electronics, but everything Kasparov did was 'just' chemistry. What, you think neurons have wit?

IBM employed several very good chess players to help develop the programming strategy for Deep (and Deeper) Blue. This is where the programming team gained the knowlege needed to enable the game to be steered into the combinatorial rather than stylistic as was commented by MyRedDice.

Still now that a computer has beaten the top chess player are they going to continue the work done with programs for GO, a much more complex proposition than chess.

I don't know - I don't think it'll be quite as much - there isn't as much media interest (in the west) in Go - so it'd be a lot harder for IBM to justify as marketing.

The amusing thing is, Go is actually, for humans, a simpler game than chess - the rules are simpler, and there isn't the requirement for unnaturally large levels of lookahead that you find in chess. But for computers it's an entirely different matter...

I wonder if chess play has gone down or up as a result of Deep Blue...

Perhaps not Deep Blue specifically. But I would guess that all the computer games for chess (like Chessmaster) with programmable levels have helped. I know several young people who have used these games to teach themselves chess. It has the advantage of being there for you whenever you like, unlike human players.