Hi,
This topic is a little old now, but if you're still interested ...
I had a go ... don't know if it's
exactly the same, but it's got the striped panels and Cassandra theme installed in LM13 mate.
I copied some files from a full install of Linux Mint 10 gnome (but you can also copy them from a downloaded .tar.gz file - see end of post).

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Short version:
From full install of LM10 (or 9) -
Copy folders
Cassandra, Felicia, Murrine and Murrina-blue from /usr/share/themes .... to usb stick .... then copy to mate install /home/yourusername/.themes
Copy folder
Felicia from /usr/share/icons .... to usb stick .... then copy to mate install /home/yourusername/.icons
Change theme to Cassandra in Control Centre > Appearance.
How I did it step-by-step:
Boot into
full install of LM10. (you may be able to extract the files from a live cd or live usb, but I don't know how)
Plug in a usb stick to copy files to. Create two folders on usb stick "Mint 10 themes" and "Mint 10 icons".
In Mint 10 -
navigate to /usr/share/themes .... click on the folders "Cassandra", "Felicia", "Murrine", and "Murrina-Blue"
Edit > copy
Go to usb stick folder "Mint 10 themes"
Edit > paste
Go back to Mint 10 -
navigate to /usr/share/icons .... clicked on folder "Felicia"
Edit > copy
Go to usb stick folder "Mint 10 icons"
Edit > paste
Exit Mint 10 install.
Boot into Mint 13 mate -
plug in usb stick with copied folders > open "Mint 10 themes" folder .....
Edit > select all (the folders Cassandra, Felicia, Murrine, Murrina-blue)
Edit > copy
Go to your /home folder
Click View > Show hidden files .... if the folder
.themes doesn't exist, then create it, then open it (note the dot before the name

)
Edit > paste
Go to usb stick again > open "Mint 10 icons" folder
click "Felicia"
Edit > copy
Go to /home folder again ....View > Show hidden files .....
if the folder
.icons doesn't already exist, create, then open it
Edit > paste
Control Center > Appearance ... both Cassandra and Felicia folders should be there
click Cassandra.
(The other folders are dependencies).
Hopefully, then you can tweak it further to look like your picture. I don't have a dock, or the oxygen icons. I assume you can add them in a similar way.
This worked for me, but try at your own risk. It might not be perfect .....
Edit: I have completely rewritten the instructions I posted originally.
When I first tried it, I copied the folders as root into /usr/share/themes and the Felicia icon folder into /usr/share/icons.
This worked fine, but I tried it a second time, just copying the files to the folders in /home/username/.themes and /home/username/.icons (as above)
and it works just the same - and is of course, much easier. So apologies for any confusion to any early readers of this post ......
Edit #2: If you don't have a full install of LM9 or 10 to copy the files from - I found all the relevant folders in this .tar.gz file which you can download and copy them the same as before from /usr/share/themes and /usr/share/icons in the .tar.gz file.
http://packages.linuxmint.com/pool/main/m/mint-artwork-gnome/mint-artwork-gnome_2.6.12.tar.gzcaribriz