It is possible to compare Windows registries between computers using a utility program called RegShot (Download HERE), but you would need to have broadly similar hardware eg both 32-bit, with similar main software installed, have a very considerable number of differing entries to compare and know exactly what you are doing to use RegEdit to set up new entries on the new computer. Using RegEdit incorrectly can very easily result in Windows not working, with no solution other than an OS install!
Personally, I wouldn't take the risk, especially on a new laptop, but if you did - Good Luck!
You can use RegEdit on the old computer to search for entries related to the program or game name and noting each entry (and exactly where it is located) found in detail on paper, but you might need to refine the search to find what the main name reference used is, and you may not find all necessary entries for the game or program to work. It is tedious to do and may take some good time before you get 'finished searching registry'. You can then manually (and very carefully) use RegEdit to set up the entries on the new computer, but be warned, some registry entries are long and sometimes very complicated! (same warning applies to knowing what you are doing, being very careful and using RegEdit at own risk to change or set up new entries!)
RegShot will run from a USB stick, and is also very useful for doing a before and after snapshot of the Windows Registry when installing software.