What do you do when you (meaning whoever is reading, or most people not specifically Abigail-II) play a game of chess? You have a knowledge of a set of openings, pick one and start. As each move results in a position you evaluate the current position, you examine the list of possible moves and evaluate each resulting position through some set of logical rules. How is this different than what a computer based chess player does? If its reliance on heuristics makes it "shallow and not very meaningful", then what does that say about the human playing chess?

As I indicated, the difference is that a computer examines all possible moves, while (good) human players only examine a few moves. They instinctly know what good moves are, and don't waste time even considering bad moves. How humans make this (pre)selection of moves to examine isn't known, but it's good enough to beat computers who can examine millions of positions per second.

Abigail

How do you think humans make this initial pre-selection? Through "knowing" which kinds of moves are generally "best", resulting in the highest valued position, from other positions. It is from memory of being in that position/arrangement before or a very similar position/arrangement. Or do you believe there is something more mystical occuring in the human mind other than rapid recognition of previous experience and logical reasoning during this process?

Is it this pruning that is the exhibition of intelligence? Or is it the fact the the heuristics are written in neurons instead of code?

I believe you have a misunderstanding regarding the heuristics used in modern chess playing programs. They do not examine all moves for the entire tree. Branches are pruned as early as they become valued such that they are determined not worth following, the system does not continue to evaluate "losing" positions and the subsequent moves.
Deep Blue employs a system called selective extensions to examine chessboard positions. Selective extensions allow the computer to more efficiently search deeply into critical board arrangements. Instead of attempting to conduct an exhaustive "brute force" search into every possible position, Deep Blue selectively chooses distinct paths to follow, eliminating irrelevant searches in the process. ( from this story)

It is a rare individual who can beat the best chess playing computers; one of the top 5 chess players in the world has tried repeatedly and has somewhere in the area of a 50% win rate against Deep Blue.