"Rain delayed the game."
Does it mean the game started late because of rain, or that the game started on time, but rain interrupted the game at some point in time?
As stated, I would infer that the entire game (the start) was delayed, but I would probably ask for clarification as to whether the reference was to the start or at some point during the game. Usually however, if the game were interrupted because of rain you might hear/read "there was a rain delay of 30 minutes before/during the game" or "rain delayed the start of the game".