The cryptic number with the 10 digits represents the so-called voucher code.
You can redeem this code on the DrawCut homepage under the "Prices/Downloads" tab.
https://www.draw-cut.com/en/prices-and-downloads/
Select the required or purchased version of DrawCut under Full version,
e.g. DrawCut PRO and click on the "BUY NOW" button.
A new window will open where you can redeem the voucher code in the left-hand field,
so that you don't have to pay for the software again.
After the voucher code has been redeemed, you will receive an automatic e-mail from DrawCut with your 26-digit PSN,
which you can use to activate the licence during installation.