Some extra commentary. Aside from all the dealing-with-loss stuff, I'm kinda thinking Jinta is a commentary against the hikikomori shut-in issue that's a thing in Japan. This is a guy that rarely leaves the house and has near-zero motivation to do anything at first. Of course he mercifully gets better as the series goes on, but this is one completely unidealized main character. I can see a secondary message of this being "Okay, you see this guy? This is messed up, DON'T BE LIKE THIS GUY". Also Jinta's got a father around the house but he's not around much and not at all proactive in getting him to go to school or otherwise break out of his funk. It takes paranormal weirdness to start that process. There isn't any commentary about it and Jinta's dad is not an important character, but I was bothered by his lightweight milquetoast personality so much that I wonder if a message was being sent there too.
Also, this is one of the shorter TV anime in existence with its 11 episode run. But it told its story and didn't feel at all incomplete, which is proof that an anime doesn't need to feel "rushed" just because it's short. There is a movie out in Japan now, I can't imagine what else there could be for it to do. But I'd bet NIS America will pick it up and we'll eventually find out.
I would suggest that it's not the medium, but the quality of perception and expression, that determines the significance of art. But what would a cartoonist know? -Bill Watterson