In order to find the Match ID of any Eternal Return match you have played, launch Eternal Return and go to the Info tab.
Then, go to the Match History sub-tab:
You can then click any match to view detailed information on it:
The Match ID of the selected match will be found centered at the top of the match information page:
You can replay any match by using the Replay button and entering the Match ID of the game you wish to view.