My understanding based on the MIDI spec is that for audio-only playback (i.e. no accompanying visual notes display), the only time information necessary to read from a MIDI file is:
The division value from the header chunk -- which is in ticks per quarter note (assuming metrical not SMPTE time)
The current tempo based on Set Tempo meta events -- which are in microseconds per quarter note
The delta-times of Note On/Off events -- which are in ticks
To determine when to start playing a note, you'd simply figure out the current real-time length of a tick by dividing the current tempo by the division (getting microseconds per tick) and multiplying that value by the Note On's tick.
Thus, if I've gotten the above correct, the separate time signature meta event information isn't needed for audio playback. Which begs the question: what is the purpose of the time signature information?
NOTE: I have asked an analogous question about key signatures elsewhere. This question is about time signatures.