I don't think we know, only that they're a son living with his father in a house that overlooks the playing fields. They didn't want to be named in the papers. I just found a slightly longer version of their account in the Express which sounds vaguer due to the inclusion of the sentence "I thought I must be dreaming":
"A witness living close to the park, who did not wish to be named, said: "I woke up at about quarter past 12 and then a few minutes later there was a scream in the distance, it sounded like a woman's scream towards the back of the park where the river bank and pond is. Then about 30 seconds later there was another scream. She must have screamed about seven or eight times. The screams must have gone on for about 15 minutes. Because of this pattern I thought I must be dreaming. They sounded eerie, they sounded dark. Then I saw a male running, but not looking back."
Libby Squire disappearance: 'Eerie' screaming heard as student vanishes
Here's the more widely reproduced version with the dreaming detail edited out:
“I woke at about quarter past 12 and there was a scream. It sounded like a woman’s scream towards the back of the park, where the river bank and pond is. Then 30 seconds later there was another scream. She must have screamed seven or eight times. All of the screams had gaps between them. The screams must have gone on for about 15 minutes. They sounded eerie, they sounded dark. Then I saw a male running."
Girl heard screaming in park just minutes after Libby Squire vanished
And the quote from his father:
"My son heard the screaming - he heard about six or seven screams - and he went to look out of the window. He said it sounded like he* was moving. It was intermittent. The man he saw wasn't dressed for a night out. He wasn't dressed for the weather. He saw him running for around 40 yards, sprinting at times. He said he was on his own and he wasn’t looking back."
Libby Squire: Police examining CCTV footage which may show missing student
(* I think this is a typo for 'she'.)