Yep, it is likely software. It is in processing the raw image data off the camera sensor, a noise reduction algorithm is applied which "smears" (essentially averages) small local pixel groups to average out grain (bright and dark specks) into more uniform values. This is something all cameras do (unless you have a RAW file straight off the sensor), it's just Apple has cranked this up to a high level in the iPhone 6 and in my opinion, they missed an acceptable balance.
Fine details get lost, particularly in areas of nearly-same values, such as foliage, cement, sky, etc. It's noticeable because, for example, on an expanse of cement, it's only the micro detail that is very similar to grain that gives it its character. If you remove that detail, you have what looks like a big sheet of beige rubber or plastic instead. And similar for fine details in leaves, for example the veins, or bark texture on branches. It also tends to show itself poorly in out of focus areas.
What we don't know if how deep this software is buried. I suppose it is possible it's actually backed into "firmware" on the camera chip, and is there even before the operating system get it. But more likely it is in the iOS software and could theoretically be adjusted. But, the fact that other apps like VSCOCam are getting the already-baked-in processing, it seems it is pretty fundamental and Apple doesn't want to give app developers access to pre-processed data. Just have to hope they see they went to far and back it off a bit in an update, or give us an option in Camera Settings (personally I would prefer more grain and less noise reduction).
I looked at your photos, and yes, that is the same effect I'm seeing in all iPhone 6 photos. Some iPhone 6 shots look excellent, some look terrible, but that over-aggressive noise processing is present to some extent in all of them. It's definitely more noticeable and more annoying in some shots than others, it really just depends on the shot: what kinds of textures are in the scene, the lighting, the focus, what ISO the camera chose for the shot, etc. And how large you view the image. Most of them look good on a small (phone) screen, but you notice the processing more on a larger screen (desktop, tv, print, etc.). Plus, some people are just a lot more sensitive to noticing (me) than others. I'm sure many people don't notice and don't care.