OK, Bill, my good friend.  This is something I threw together for you tonight in a hurry, so it is not polished nor comprehensive.  My beliefs on this subject are not a result simply of observed verse, but many comparisons of terminologies and ideas in scripture, coupled with my experience and knowledge of God as He has revealed Himself to me.  I cannot here present this whole progression nor elaborate much on my thought processes, but this will be enough for a framework.  The order and transition of ideas here may not be the most ideal, so please read everything first, and then go back and compare.  All scriptures are NIV except where noted.

First, regarding the scripture you asked about: reference Psalm 104.   The psalmist is speaking about the land and sea creatures of the earth.   He is referring to the breath/spirit of animals using the Hebrew word ruach, which is also used extensively for the breath/spirit of man and for the breath/spirit of God.  In verses 29-30, the words translated breath and spirit in English are this same Hebrew word ruach.  I have replaced them accordingly.

When you hide your face, they are terrified;
when you take away their ruach, they die and return to the dust.
When you send your ruach, they are created,
and you renew the face of the earth.

First notice that God takes away ruach, and sends ruach.  It doesn’t say he destroys ruach; he takes it.  It doesn’t say he creates ruach; he sends it.  We will see this terminology in another scripture later, speaking of both “taking back” and “gathering to himself.”  More telling, though, is the lack of terminology portraying destruction or creation of ruach in scripture.

Now check out the literal Hebrew below. 

    you hide faces of you
    they are terrified
    you take away ruach of them
    and to dust of them they return
    you send ruach of you
    they are created
    and you renew
    faces of earth

Notice the cool parallelisms!  Notice the juxtaposition of:   
      
    faces of you (God)
    faces of earth (creatures)

    ruach of them (creatures)
    ruach of you (God)

Also notice the reference to “dust of them” and “ruach of them.”  We will talk more about this later.

About dust and ruach:

Ecclesiastes 12:7
...and the dust returns to the ground it came from, and the ruach returns to God who gave it.

In Genesis 6:17, we see ruach used to refer to the breath/spirit of all life on earth, both man and animal:

I am going to bring floodwaters on the earth to destroy all life under the heavens, every creature that has the ruach of life in it. Everything on earth will perish.

So, one might ask, what is the unique quality man has been given above the animals?  

In Genesis 2:7:  The LORD God formed the man from the dust of the ground and breathed into his nostrils the breath of life, and the man became a living being.

Or, in the KJV: And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.

It is important to note that “breath” in the verse above is NOT ruach; it is the Hebrew n’shamah, which means breath somewhat more literally.  The word soul/being above is the Hebrew nephesh.  This soul is the distinction applied to mankind here.  But notice, the narrative doesn’t even use the word spirit (ruach) anywhere in making the distinction.  Man is something different indeed, but he is referred to as a soul/being in explanation of the uniqueness.  The other and most notable distinction in the creation account is the reference to man being made in the image of God.  Of course this has nothing to do with the ruach terminology either.

As you see, the terminology used to portray mankind’s distinctness/uniqueness above the other animals does not in any way preclude the idea of the eternality of the ruach of non-human life.  Furthermore, the understanding of everything existing in God is in full harmony with the understanding of ruach returning to God and the impossibility of its being lost.  

The scripture below speaks of ruach, n’shamah, and dust.  (Please note that this is Elihu speaking, NOT one of the three men rebuked for speaking incorrectly about God.)

Job 34:14-15 (NRSV is best here)
If he should take back his spirit (ruach) to himself,
and gather to himself his breath (n’shamah),
all flesh (basar) would perish together,
and all mortals (adam) return to dust.

Again we see both the ruach and the n’shamah return to God, as all flesh returns to dust.  Nothing is lost.  The flesh undergoes a chemical decomposition, which we perceive as “perishing” or destruction, but in reality, all the elements remain and are not lost.  Likewise, the body/spirit “compound” undergoes a similar sort of deconstruction.  The life force apart from the body is unrecognizable to us, just as flesh that has been completely decomposed back to the earthly elements is unrecognizable to us.  The former is invisible to our earthly senses; the latter is unrecognizable as the living body it once was. Neither is truly lost.  It is we who have lost them.  The multitude of scriptures regarding resurrection, transformation, re-creation, and restoration address God’s ability and promise to reconstruct what has “perished” in this sense.

Revelation 21:4-7 NKJV:
"And God will wipe away every tear from their eyes; there shall be no more death, nor sorrow, nor crying. There shall be no more pain, for the former things have passed away."
Then He who sat on the throne said, "Behold, I make all things new." And He said to me, "Write, for these words are true and faithful."
And He said to me, "It is done! I am the Alpha and the Omega, the Beginning and the End. I will give of the fountain of the water of life freely to him who thirsts.
"He who overcomes shall inherit all things, and I will be his God and he shall be My son.”

Those animals we love
which have touched us so deeply
and caused us to glorify God in our lives
are certainly real
and certainly things
and all things certainly includes them

I believe

as Adam named the animals
brought to him in the garden by God
that God created
for Adam’s dominion on earth
in fellowship with YHWH
even so
the child of God names the animals
brought to him in his life by God
that God created
for his eternal dominion
in the presence of YHWH

So call me a looney...