@TalJechin, 

I appreciate your desire for a succinct definition of "classical style", but the meaning has morphed over time.  Before WWII, "Classical style" was pretty much as MNb describes it.  However, since the advent of dynamism as its own style, Classicism has become a term which differentiates types of dynamic play.  I return to my original definition:

Classicism in chess, as in art and architecture, is a style that seeks straightforward development, clean lines, and a minimum of chaos.

Your definition suggest that dynamic chess players are not interested in finding the best move.  Computer chess is certainly NOT classical, yet Hydra also seeks the best lines.  Style is not about finding the best lines, it's about determining what criteria to use for "best".  Human styles are mostly aesthetic approaches.
Computer chess is purely utilitarian.

Spassky had in mind  something other than pure "classicism" when he spoke of "a strict classical profile".  Spassky was describing Fischer's style as an answer to the dynamism of the Soviet School (which has its roots in the play of Chigorin). 

Fischer introduced a sort of "neo-classicism" to chess which integrated the findings of the hypermoderns and the concrete analysis of the Soviets into a system which sought "clean" solutions to chess.  One fantastic example of this was in game 7 of his Candidates' match against Petrosian.  Fischer had an edge with a strong Knight dominating a weak Bishop.  He shocked all the analysts by trading it off (22.NxBd7!!) and heading for a simple win.  Black resigned on move 34. Very few players at that time would have even considered such a move. 

By the way, my original definition is only 21 words long, 

[Classicism is] "a style that favors straight-forward development, a preference for "clean lines" over chaotic ones, and activity over defense."

yours is 26.  Succinctness doesn't preclude accuracy.

The usual meaning of the classical versus modern antithesis is indeed occupying the centre with pawns versus controlling it with pieces, especially by fianchetto('s). The main advocate of the classical style was Tarrasch of course. See his comment on Capablanca-Spielmann, New York 1927: 1.d4 d5 2.Nf3 e6 3.c4 Nd7
"Einer von den krümmen Zügen, die jetzt so modern sind." I hope my translation is correct: "One of those crooked moves, which are so modern now."
The main advocate of the modern (anti-classical) style was Nimzovitsj of course, though I must mention Réti too. One might say, that Petrosjan applied Nimzovitsj' ideas in extremo.
When we look at the openings of their 1969 match, we see that Spassky played the Tarrasch (!), the QGD and only once the Nimzo-Indian - with which he lost. Also with White Spassky chose openings with smooth development and centre control with pawns.
So we might say, that Spassky beat Petrosjan with classical chess, though not that strict. Game 17 saw Spassky employ a queen's fianchetto at move 9.

I must say, that I find the classical-modern antithesis not very useful. Eg Tal already in 1952 opened 1.c4 followed by a king's fianchetto. Another player with the socalled classical style was Frank Marshall. On Thomas Johansson's website one can find an article on Marshall playing the Queen's Indian as Black.
Finally my hero, the last knight of (the very classical) King's Gambit, already in 1912 (before the revolution of the modernists) defeated Rubinstein in a modern style. Spielmann played some kind of Benoni with his king's knight to e7; subsequently he preferred to play Kf8 in stead of castling. The result was a crushing attack against Rubinstein's poor king. So who's modern and who's classical?

Was reading a book abt Spassky some time ago by Barden (batsford). In the introduction there was  part in which Spassky discusses his match strategy to beat Petrosian "to play in a strict classical profile". In it he also says that Petrosian is not a master of strict classical profile. Elsewhere (or perhaps in another book) it mentions that Fischer is a player of strict classical profile.
 
What does this "classical profile" mean?? Does it mean that the player plays by applying the ideas of Steinitz, Chigorin and Tarrasch?? Or does it mean that he plays in a way such that his opening system  always involves exerting pressure on the center by pawns rather than pieces?? Or does it mean that his style has a resemblence to the style played by the gambiteers or romantics eg Andersson, Morphy, kieseritzky, blackburne & pillsbury?? Or is it all of the above.
 
thanks