Nice clicks and a great video you shared A.I is definitely taking over

I'm no expert, but upon closer perusal, appears to be a FILA, circa 2012, most likely a *Pegasus Elite II*, mid-distance runner.  

Women's, size 7 or 8, suggested  by the length-to-width, ball-to-heel ratiotics of extent.  {R.E. = 12 - D/[bh]²+3 }.
 
Though there is some superficial algae on the outer surfaces,  complete lack of moss growth and the still-supple inner arch have me leaning toward shoe mis-placement in the month of September, maybe the second or third week? 

Hard to say which day, as I am not privy to your exact location of discovery, or daily weather patterns for that month in your area. 

Owner was a minor Supinator, by the look of starboard cushion collapse and insert wear at the apex of the heel.  Orthotics would help in this regard, but are obviously not present. 

The fact the laces are completely missing is key here. No wild animal in your part of the world is yet capable of fully removing the entire lacing in a double-sided, 7 hole design shoe, particularly on a pair with loop-stitch eyes in the upper 2/3 shoe-drant (tech-speak for shoe/quadrant, for you podiatric analysis novi out there.) 

The lack of lacing, and the fact the tongue is distended in the Beta position, suggests rapid  egress from the shoe, possibly from one of two scenarii:

Scenario 1.0) Owner needed to exit shoe in rapid form, such as in an emergency situation. I can not tell if the laces were cut, as the distal side of the tongue is not visible, and would show major sharp-implement lacerations to it's outer integument, if performed in a rapid, emergency exit. 

I am leaning away from this scenario, as there would no-doubt be a few lace-segments still present in at least one or two eyelet openings. 

Though upon second thought, rodents of the genus Neotoma (common Pack or Wood Rat) HAVE been observed pulling and thus utilizing leftover lacing from emergency shoe situations as nesting materials in their birthing dens. 

These crafty creatures COULD have pulled the leftover lacing for this purpose. Question here: Did you see any Pack Rat evidence in the area?  Do you know the gestation dynamics of this species in your part of the country?  This would be most helpful. 
 
Scenario 2.0) The owner of said footwear decided to discard the shoe, and being a thrifty individual, PULLED the laces from the shoe, in hopes of using them for some other, unknown  household application. 

Possibly to tie-up a package for mailing in the US Postal system? Hang old bicycle inner-tubes from the rafters of the garage? The possibilities are endless.  

Once laces were pulled, the owner then decided to abandon the shoe out into the wilderness, to allay any garbage disposal fees imposed upon them at their domicile of existence. This is where our scenario diverges on the path of possibility. 

Scenario 2.0a) The shoe was transported here by the owner during a recent hike or camping trip. 

The fact there is only ONE shoe suggests they are generally a law-abiding citizen, and not wanting to incur the large fines in place for Abandonment of Footwear onPublic Lands, distributed the shoe pair separately across the landscape. 

(Have you considered traveling out once more to the woods, to try to locate the mate to this shoe?  It would give us more information with which to complete further analysis.) 

OR:

SubScenario 2.0b) Waterway motility:
I am not privy, once more, to your exact shoe location, regarding proximity to waterways or flood-planes, as this would suggest the shoe was transported to it's current location on water-borne currents, AFTER initial, dry-land discard. 

Once again, my theoretics lean away from this direction: The surrounding leaves of the area show no sedimentation or deposition of non-native vegetational detritus, and likewise there is no earthen sedimentation within the shoe itself. Only wind-born needles and aero-born frass from the upper-level reaches of the conifer trees of the area. 
  
Final Analysis and Thoughts:  
I really have no idea where this shoe might have originated. But I do hope you took it home, as it still shows ~47% of it's original footwear life still intact, and you could definitely get some more wear out of this fine-ly crafted shoe.  Plus the color is pretty darn spiffy. 

Like I said, I'm no expert. But I am glad to see someone else posts about errant shoes. It's a lonely road to hoe, but someone has to do it.

Eek that looks so alien? On the subject of the missing pair of shoe, do I smell a fiction series? Hmmm :D It's very interesting to speculate about it.

My theory on the slipper in the woods is that teenagers are sometimes very careless with things.  They occasionally put their tubas on top of slippers and then drag the tuba out of the car in a big hurry in the morning when dropped of at school.  The slipper then falls on the street without anyone noticing.  Other teens (or perhaps dogs) pick up the slipper and carry it into the woods pretending it is some sort of game of 'hide the slipper'.  LOL.

It seems that adventure people's shoes to the mountain by leaving shoes, then come someone else to get the shoelaces. That's my guess