God as a non-empirical being

[noctalla]

I recently had a debate with a theist who made what I thought was a strange claim. In response to me saying I saw no evidence for a God, he asserted: "God is not an empirical being, so asking for empirical evidence is a simple category error." Although I pressed him to explain what he meant by this, all he did was to repeat the claim in various ways without elaborating or giving an argument to support it. Despite the fact that I had not said the evidence had to be empirical in nature, I felt the claim that God is not an empirical being needed to be justified. I said that empirical evidence requires observation and experience. If a God exists, I saw no reason we could not observe or experience said God, therefore this is not a category error. The theist eventually lost interest and stopped replying.
I was wondering:
1. Has anyone else had encountered this claim?
2. Is there an argument that supports this claim?
3. What are the counterarguments?