How do I replace one switch in a 2-gang box with a timer?
The current set-up with the wire bent into a loop and the same wire proceeding on is perfectly fine. You do not have to have separate pigtails for each switch. I have one 3-gang switch box where I used that connection method for the three switches. The city electrical inspector said it was fully acceptable.

EDIT
But it could be that the installation of the new timer switch would be easier if the two switches were each fed by a separate pigtail from the line hot. Sometimes these timers have stranded wire leads and sometimes they have hard contacts. What does yours have?