He's playing Lachrimae, by John Dowland.
Flow, my tears, fall from your springs!
Exiled for ever, let me mourn;
Where night's black bird her sad infamy sings,
There let me live forlorn.
Down vain lights, shine you no more!
No nights are dark enough for those
That in despair their lost fortunes deplore.
Light doth but shame disclose.
Never may my woes be relieved,
Since pity is fled;
And tears and sighs and groans my weary days
Of all joys have deprived.
From the highest spire of contentment
My fortune is thrown;
And fear and grief and pain for my deserts
Are my hopes, since hope is gone.
Hark! you shadows that in darkness dwell,
Learn to contemn light
Happy, happy they that in hell
Feel not the world's despite.
It's the seventeenth century version of this:
The Sky Is Crying, by Elmore James
The sky is cryin'
Can't you see the tears roll down the street
I've been looking for my baby
And I wonder where can she be
I saw my baby early one morning
She was walking on down the street
You know it hurt me, hurt me so bad
Made my poor heart skip a beat
I've got a real bad feelin'
That my baby she don't love me no more
You know the sky, the sky's been cryin'
Can you see the tears roll down my nose
Gary Moore wasn't fooling. Drank himself to death in 2011.