This is an interesting question as I have never used that Interface. You are right there is no help in the API about this, in fact a quick Google returned this question as the top ranking page about IESRIScriptEngine! So I'm guessing no one in ESRI or the entire planet is using this interface other than you Roland! You are clearly ahead of the curve!
So I tried to have a play and I could not even create the object, it would return a Com Exception error on the second line
Dim pESRIScriptEngine As IESRIScriptEngine
pESRIScriptEngine = New ESRIScriptEngine
I've not attempted to delve too deep into this but this page suggests one possible cause is that it is referencing other DLL's. As there is no information, no discussion (other than this page), no advice, no sample code, nothing about this Interface I wonder if it is sensible to continue with it?
This page talks about running arcpy from within a .Net application, may be that is the way to go?