Actually, yes. This statement is all-inclusive. That is, any truth there may be would be non-absolute (meaning, it would be a rule with exceptions). If so, it is itself an absolute claim. And of course it contradicts itself. Which means there must be at least one absolute truth

Being emphatic is nice, but unfortunately it doesn’t make up for errors in the argument.
You’re speaking about absolute truth in the sense that it encompasses everything. He was speaking about absolute truth in the sense of absolute certainty (since that was what my claims, which his question addressed, were dealing with).