If you have registered your product with Magix then you may be able to download it from your Magix account if you go to your registered products page but if not, get a cheap USB DVD player from Amazon. I don't know where you are in the world or if you are in lock-down or not but in the UK you can still order and get deliveries through Amazon.
First, assuming your new computer uses Win 10, be aware that MEP 2015 may not run without problems.
Second, and simplest answer to your question: buy an external USB DVD Rewriter (they're pretty cheap). Once connected to your computer its will be seen by Windows as a CD/DVD drive. Insert your program disk and install MEP.
Third, if you don't want to buy an external drive, assuming your "old" computer has a CD/DVD drive and is still accessible, put the CD into its drive and select to copy the entire content to a suitably-sized USB Memory Stick. Once finished, put the same memory stick into your new computer, open it to view its content, double-click on the installer (likely to be "install.exe" or "setup.exe" or similar) and the program will be installed.
One other thing: in order to avoid any potential problems of authorising the new install, make sure you deactivate the installation on your old computer before you begin the installation on your new one.