Yep.. battery swelling for sure. Looks like the bottom is swelling also since it is not sitting flat in the desktop.
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Good advice. Or if he's comfortable popping the back off he could replace the battery with an OEM battery from iFixit to save a little money.Mac Repair and Service - Apple Support
Need to repair your Mac? See your service options, their costs by coverage type, and how long they take.support.apple.com
You could use Apple's flat rate $199 repair for this. I think it would be worth to keep that thing going another year or so.