No, it's not limited to binary trees. Yes, pre-order and post-order can be used for $n$-ary trees. You simply replace the steps "Traverse the left subtree.... Traverse the right subtree...." in the Wikipedia article by "For each child: traverse the subtree rooted at that child by recursively calling the traversal function". We assume that the for-loop will iterate through the children in the order they are found in the data-structure: typically, in left-to-right order, for a diagram such as you have shown.
In fact, this is already described in the Wikipedia article on tree traversals: see https://en.wikipedia.org/wiki/Tree_traversal#Generic_tree, which describes exactly how to generalize this to $n$-ary trees. Pre-order traversal is one where the pre-order operation is "Display the current node" and the post-order operation is "Do nothing". Post-order traversal is one where the pre-order operation is "Do nothing" and the post-order operation is "Display the current node".
In-order traversal is a special case. It probably only makes sense for binary trees. While there are several different possible ways that one could define in-order traversal for $n$-ary trees, each of those feels a bit odd and unnatural and probably not terribly useful in practice. So, it's probably best to think of in-order traversal as being specific to binary trees; if you want to do something akin in-order traversal for a $n$-ary tree, you'll need to decide exactly what you mean by that, as there's no standard meaning for that.