MarkReeder

const headers = {};
const songs = [];
document.querySelectorAll('tr').forEach(row => {
    row.querySelectorAll('th').forEach((headerElem, i) => {
        headers[i] = headerElem.innerText;
    });
    const song = {};
    row.querySelectorAll('td').forEach((bodyElem, i) => {
        song[headers[i]] = bodyElem.innerText;
    });

MarkReeder

right-click somewhere on the page and click inspect element
click on the Resources tab
open the Local Storage item and click turntable.fm
right-click, edit on the value portion of TFMEXsongTags
copy that, paste it somewhere and get it to your other machine

Then do the same thing on your other machine except paste the value of TFMEXsongTags instead of copying it.
You'll need to tag something on the new machine (doesn't matter what it is, it will get over written when you
paste the other value in) or create the TFMEXsongTags key yourself.