Let's say his name is Sven.
Han ser sig själv. = 'He sees himself' = Sven sees Sven
Han ser honom själv = 'He sees him himself' = Sven sees Björn (with his own eyes)
Han ser själv = 'He sees [by] himself' = Sven sees with his own eyes
själv can belong either to ser – in that case ser själv means 'sees [by] himself' or 'sees [with his own eyes]'
or själv can belong to sig, and then it refers to the person who is being seen.
There is no ambiguity in Swedish here, but there can be in English if you say He sees himself.
Am I correct in thinking that Han ser sig själv is a combination of "He sees himself" and "He himself sees"?
If so, then maybe a more literal (but clumsy) translation of Han ser sig själv into English would be He himself sees himself (which, admittedly, doesn't sound like very good English).