As a result, we play ball indoors on rainy days.

Literal

Result, rainy days [topic-は] room [genitive-の] inside [at-で] ball-play [object-を] doing [progressive-ている].

結果 ('result') at the start of a sentence, without a particle, means 'as a result, consequently' — a discourse connector more formal than だから. 雨の日は functions as the temporal topic ('on rainy days, ...'). ~ている here is the habitual use — 'we (regularly) play ball,' not 'we are currently playing ball.' This habitual ~ている is distinct from the ongoing-action reading.