upon inspection the Note On Message doesn't include the Delta-Time. So, how do I specify the Delta-Time for each message?
Although most MIDI sequencer software will show a note as a single event that contains a duration value, be aware that the actual events in the MIDI file (and the actual messages sent to a MIDI port) use one message to start the note and another message to end the note:
In MIDI, you start a note with a Note On message with non-zero velocity.
You end a note with a Note Off message or a Note On message with zero velocity.
Your example MIDI file only contains note messages that start notes on Channel 10. It's true that when sending Channel 10 percussion notes to a MIDI device, most devices will produce the correct drum sounds and not care if the messages to end the notes are missing. However, you are supposed to always include a message to end each note, so that anything else that processes the MIDI file or the MIDI port's message stream can tell the note ends.
MIDI 1.0 Detailed Specification, Appendix section "Assignment of Note On/Off Commands" on PDF page 67 / printed page A-4: "The transmitter [...] must send a corresponding Note Off message for every Note On sent."
General MIDI System Level 1 Developer Guidelines section "Response to Note-off on Channel 10 (Percussion)" on PDF page 19 / printed page 15: "The MIDI Specification requires that all Note-On commands have a corresponding Note-Off command, and it is assumed that all MIDI transmitters will comply with this requirement"