Hey! You shouldn't need to sign up with Mega just to download. It should do a "pre-download" and then actually download the file really quickly once it reaches 100%. I dunno why it works this way, it just does. I hope this helps!
Whenever I click download I get a pop-up that says "you are not logged in"
When i try it i get the choice: open in Mega App or Open in Browser. Choose open in browser and you shouldn't have any problems.