I tend to agree with the previous poster, though I would add that the loss of the tiger has a global impact only because we won't see this wonderful anymore. But that is really not an important or lasting effect. The fact is that species actually go extinct pretty regularly and it is not always because of human destruction of habitat, etc. Now, in this case it was so people feel the need to get up in arms about it, but there is a limit to the usefulness of defending a certain animal simply for the sake of defending it.
At least in this way the black market for Siberian Tiger products will get shut down, but that is not a global issue either as it certainly wasn't a large enough market to have any global impact.
In my opinion, there are no global effects or at least none that we can really understand or quantify.
When a species of animal goes extinct, it rarely has any effect on people, per se (unless they rely on it for food or to keep an ecosystem in balance). The only real impact of extinction is on the other animals (and even plants) in the ecosystem. You could say that tiger extinction could lead to a boom in deer which would then affect the forests. But the loss of tigers is being caused by deforestation anyway -- whole ecosystems being destroyed. So it's not as if the ecosystem will still be there but be imbalanced by the loss of the top predator.
What does have a global effect, in my opinion, is the habitat loss that leads to the extinctions. The loss of whole habitats can affect weather patterns on a regional or even global level. It can also impact people (potentially) through the loss of biodiversity and through the loss of organisms that might be beneficial to people. However, even these impacts are hard to distinguish since the planet as a whole is such a complex system.