I’m not a really a chess player but I’m curious about Viktor Korchnoi’s playing style. Is it true that continuously pressing an attack creates more possibilities after each move, which the defender will find harder to counter? Let’s just define an attack: you steadily position your pieces in closer proximity to the opponent’s king in order to threaten a mate, or even just a check. My off-the-cuff answer to myself is “any move creates x-many possibilities.”
The number of possibilities available is based on the total number (and types) of pieces under your control. Losing your queen could, in just one turn, remove as many as 21 possibilities. Over the life of a game, the total number of possibilities that a queen enables is probably a cosmic number.
If your opponent is able to make a successful attack, the loss that you take is a significant disadvantage that will, probably, lose the game for you (ignoring the loss of a few pawns), because your possible moves each turn is significantly reduced compared to your opponent’s.
To avoid that, you have to move to prevent the attack. But this also means that your possibilities, during your turn, are reduced. Specifically, your only moves are the ones that prevent the attack. One might say that this also puts the attacker at a similar disadvantage, since he is going to want to complete the attack and will, thus, need to move so that attacking is still possible. But that doesn’t hold because the attacker chose when to start attacking and he can always choose to let you go free. So while both parties are, to some extent, constrained by the interaction, on the whole the attacker is going to be the one who had the most control over the flow of the game.
Nice one. So does it really make sense to focus on a good attack each time?
Garry Kasparov is also a great attacker, who may give up material to gain mobility. You can see some his attacks on YouTube, eg. a stupendous sacrificial attack called Immortal.
There are different kinds of attack in chess; it’s not true that in all cases the attack will, or is intended to, reduce the number of options the opponent has.
And in chess the term “attack” is a little more broad than as defined in the OP: I may calculate a combination that nets me a couple of pawns, and then my plan after that could be to retreat my capturing piece to a safe position. That’s still an attack, just a standalone one.
But yeah, I’m quite fond of attacks where you slowly make positional gains and give your opponent fewer and fewer options. One of my favourite players is Tigran Petrosian who had many great wins in this style – I’ll try to find one of his better ones for you.
In my own games I have had opponents resign when I was as little as a pawn up with no obvious way to win material or mate for some time to come. I had just managed to squeeze their position so much they just didn’t want to play on. 
And I’ve been on the other side of it, of course. It’s frustrating, but always worth playing on IMO; just a couple of trades and the position can suddenly look equal.
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Moving thread from General Questions to the Game Room.
Most chess attacks do not fit this definition: A queen, rook or bishop need not be in close proximity to be a threat, and threats that have nothing directly to do with the opposing king can ultimately lead to his checkmate.
In principle, staying continually on the offensive will eventually win you the game. In practice, of course, it’s never that simple: An opponent might make a single move that defends both against the current attack and against the attack you would have made the next turn, thus breaking your streak. An opponent might even be able to make a single move that stops your attack and counterattacks you at the same time. One does occasionally see high-level games where one player carries on a very long string of continual attacks, often gaining something of value in the process, but how do you set up for that? Being able to pull it off is what makes those guys the masters.