What could cause water to not go into the gutters

Oh, wow. I'm sorry, but your roof is probably bad. If you can get the money you paid four years ago back (doubtful), I would, but you probably need to get that entire mess torn off all the way down to the decking, and probably quite a bit of the decking near the edges of the roof too. You can tell because the shingles look "lumpy" and have a rolling look to them -- like someone's melted them, especially near the edges -- and the valley is curved instead of sharp. I can also see the lines running across where different runs of roof sheathing panels meet (every 4' or so); that it's sagged in between these lines is a sign of sheathing damage.

Your roof isn't the shingles, so it doesn't matter that the shingles are only four years old. Your roof is actually the tar paper and ice and water shield that is underneath underneath the shingles. Multiple layers of shingles are bad; it means that they didn't replace the actual stuff that keeps the water out of your house, they just replaced the stuff that you see that goes over top.

If you go up into your attic when it's been raining quite a bit, see how much more of the underside of your roof sheathing is damp. If there's a lot, you need to get it torn off and replaced as soon as possible. If there isn't much, you have a few years to save up for it, but it looks bad now from the top. Make sure when they re-do it that they tear everything down to bare wood, remove all the nails and staples and junk, use Ice & Water Shield along the roof edges and in the valleys, and then put new 30 year tar paper and shingles over it. The tar paper and ice&water shield is what actually keeps the water out of your house. The shingles only protect the tar paper from abuse.

Hardness is a good way to check wood for damage without pulling it apart. Take a nail and press it into the wood where you know the siding is in good shape. Then, do the same where you suspect damage. If the wood is softer, then you can assume it has some amount of water damage. If you want a more direct, verifiable method your best bet is to yank a shingle or two off and check behind them. (From the pictures it looks like you have shake but its hard to tell.)

Also, as Steven commented...remove those "gutters" as soon as is humanly possible and replace them with actual gutters. Each year you wait things will get exponentially worse. If there is not currently water damage (which I doubt, sorry) there will be very soon.