Can one show participantID on event reminder?
Unless writing an extension implementing token processor its not possible to fetch the participant id in reminders.
If you familiar with smarty and the contact will have only one participant for a event than you can try below snippet in your reminder message template
{capture assign=eventID}{event.event_id}{/capture}
{capture assign=contactId}{contact.contact_id}{/capture}

{crmAPI var='result' entity='Participant' action='getvalue' sequential=0 return=&quot;id&quot; event_id=$eventID contact_id=$contactId}
{foreach from=$result.values item=participant}
 Participant Id - {$participant.id}
{/foreach}