I'm not a Suunto user, so cannot verify or test any of this, but: did you download / export from Suunto App "Routes"? Generally "routes" have no timestamp data, because they are just Routes (where did you go), not Activities (where and when).
Or describe your process ("Suunto-generated GPX file" creation steps) in a bit more detail, and perhaps we can get to the bottom of this. Other Suunto users may be able to guide you with the steps to get a properly-timestamped GPX file for use with RG/RG2.
I'm fairly sure that if you
link your Suunto App account here on AP, you'll then be able to download from AP useful-for-RG/RG2 GPX files.