What you're asking to accomplish here is a bit tricky, because you want to create subdirectories on-the-fly as needed. Not impossible, for sure, but a bit more tricky than a standard find . -name pattern -print or similar.

To make sure I got this one right, I created a simple directory hierarchy of my own for testing purposes, using mkdir and touch. Then I experimented with both the tar and cpio commands...

Before I show you the results, let me say that if you haven't poked around with the cpio command, you should, because it has one great feature that standard tar lacks: it can read a list of filenames from standard input, which makes it an excellent partner to the find command. Some versions of tar can read from stdin, but why it's not a standard part of the command I still don't know. It's not that hard to do...

Anyway, I digress. Here are the two commands I used to create a test heirarchy:

$ mkdir test test2 test/a test/b test/c
$ touch test/a/{x.x,x.y} test/b/x.y test/c/x.x

Running a recursive ls produces this:

$ ls -R test test2
test:
a/      b/      c/

test/a:
x.x     x.y

test/b:
x.y

test/c:
x.x

test2:
$

Now, the challenge you've posed is to be able to copy all the "*.x" files into the new directory, building any necessary subdirectories required as we go. The first solution is to use tar and create an intermediate backup file:

$ cd test
$ tar cvf test.tar $(find . -name '*.x' -print)
./a/x.x
./c/x.x
$ 

This slick command (the command in the $( ) sequence is run, then its output replaces it on the command line before the tar command is actually invoked) generates a file that we can then easily unpack in the "test2" directory with a simple tar xf test.tar. But. But it's not an elegant solution because we don't want to use an intermediate file, plus there's a finite limit to how long a command line can be, and you could easily exceed it here. I know we could use two invocations of tar to copy a directory tree without producing an intermediate archive file, but the command line length limitation would still be lurking.

So instead, here's a much more pleasant solution using cpio instead:

$ find . -name '*.x' -print | cpio -pavd ../test2
/Users/taylor/Desktop/test2/./a/x.x
/Users/taylor/Desktop/test2/./c/x.x
$

And, finally, here's the new heirarchical directory list of "test" and "test2", showing that the latter now does indeed have only the "*.x" files and all necessary subdirectories required too:

$ cd ..
$ ls -R test test2
test:
a/      b/      c/

test/a:
x.x     x.y

test/b:
x.y

test/c:
x.x

test2:
a/      c/

test2/a:
x.x

test2/c:
x.x
$

I bet that'll give you the information you need to accomplish your file copying task, somehow. A fun problem to solve!