The PNG thing is a big fat myth. You never need PNG for printing, don't worry.
The first question is: "Do you have the rights to use this image?" Simply because you CAN download an image from the web and put it into Photoshop, doesn't mean you're ALLOWED to do so. Make sure you check on that.
If you are satisfied that it's ok to use, then we turn our attention to the file itself. It's only 1103 pixels wide. If we assume that print resolution is 300ppi, then this image is only printable at 3.67 inches wide (ironically, that's barely bigger than an actual passport photo). I rather suspect you'd intended to print it larger than that.
People will tell you, and they're right, that it's perfectly possible to enlarge a file beyond the rigid mathematical calculation that I made above. However, such enlargements are dependent on the quality of the file, and there we come to the second problem - this is a very damaged file. It has clearly been saved with very aggressive jpeg compression. So I'm not sure I'd even trust it to print nicely at 3.67 inches wide, let alone larger.
So, I'd urge you to do one of the following:
Contact the owner of the image, if it's possible to find them, and ask to purchase a higher-resolution version of it.
Go to a reputable stock image site such as shutterstock.com or istockphoto.com and search for "world map". You'll find lots of amazing options to choose from, and not too expensive.