Trashing an opponent's gold is a very close approximation to gaining a gold for yourself.
That's already not very true in 2-player Dominion and becomes even more inaccurate as you increase the number of players. DotA / LoL is 5v5 and an analogous choice has very different results. In DotA, denying presents the choice of "do I get +gold or do I prevent
1 opponent from getting +gold".
Let's look at what this means. It's a hyper-simplified analysis but I think it illustrates the difference:
Let's look at a hypothetical four-player MOBA game. Let's say everybody kills a creep for 5 gold every X seconds. With no denying, everybody in this fairy-tale game advances in lock-step gaining gold, like so:
Player 1 (Team 1): 5, 10, 15, 20...
Player 2 (Team 1): 5, 10, 15, 20...
Player 3 (Team 2): 5, 10, 15, 20...
Player 4 (Team 2): 5, 10, 15, 20...
Now let's say each player has the option of forfeiting a creep kill to prevent an opponent from gaining 5 gold. Player 1 decided to do this to player 3 for the first two creep waves and the rest continue on naively. The only difference for player 3 is that he tries to kill those first two creeps and misses because player 1 denied him.
Player 1 (Team 1): 0, 0, 5, 10...
Player 2 (Team 1): 5, 10, 15, 20...
Player 3 (Team 2): 0, 0, 5, 10...
Player 4 (Team 2): 5, 10, 15, 20...
Now, you might say "the teams have the same overall gold now" but
distribution of gold is very important in a MOBA. You want to guide the money to your item-dependent characters so they can get those crucial items as soon as possible. Player 3 is now behind the curve because of Player 1's sacrifice. If player 1 is a support / utility character, he doesn't need as much gold anyway; Team 1 is now in the "lead".
And the reality is much more complicated than this. There are 5 opponents in DotA and you have lots of competing choices all the time. When choosing to last hit or deny, you have to ask yourself if you want to gain gold relative to 5 opponents or keep just one of them down. The answer depends on your role and the situation.