There are two parts to this: 'out of' and 'space'.
Especially in contemporary American English, 'out of' is often used to mean 'in', for example "I work out of Atlanta" means I work in Atlanta; if I am writing out of a particular space, it means I am in that space while I am writing.
'Space' has many meanings, one of which is 'place', for example "I need a space to work" means I need a place to work. Here, the context clearly shows that the word is being used to mean a state of mind, and/or a situation.
In other words, in describing the space he was writing out of, Thomas was describing the state of mind he was in when it wrote it.