From DIAA handbook, here are pitching rules:
A. A player may not pitch in more than 16 innings in any seven calendar day period. Delivery of one pitch constitutes having pitched in an inning.
B. If a player pitches in three innings or less in a day, no rest is required before he/she pitches again.
C. If a player pitches in four, five, or six innings in a day, he/she must have two calendar days of rest.
D. If a player pitches in seven or more innings in a day, he/she must have three calendar days of rest.
E. This regulation is in effect for both regularly scheduled tournament games and games that were postponed or suspended for any reason. It also applies to any playoff games that are under the jurisdiction of the Committee.
So, it sounds like Archmere pitcher could not pitch Wednesday, but Dover pitcher could.
Also, about the schedule (also from DIAA site), the games will be played Thursday, as scheduled, assuming the quarterfinal games are completed Wednesday. It's not clear what will happen if quarterfinal games carry over to Thursday (more rain expected Wed and Thur). It appears everything would get bumped a day, making semifinals Friday. Finals Saturday or Sunday, anyone know?