Can an Indian national currently working in Saudi Arabia apply for a Philippines visa from there?

Yes, if you are in Saudi for 3+ months as of now, you can apply in local Philippines embassy. I will explain my experience in Doha.

You need standard documents like bank statements, confirmed flight tickets, hotel bookings, ID card copy, NOC from employer (at least in Doha), and PCC if visiting first time.

Once you get visa, you could use it from India, there is no restriction of boarding point on visa.

Quote from Philippines Embassy in Riyadh Visa Section (Note: Auto PDF Download at page visit)

List of Requirements for Non-Immigrant Visa

1. Personal appearance;
2. Passport valid for at least six (6) months beyond the applicant’s stay in the Philippines
3. Two (2) photocopies of passport
4. Duly accomplished Visa Application Form (FA Form No. 2) and one photocopy;
5. Two (2) colored photographs (2 X 2 size) with plain background;
6. Letter request from sponsor / employer stating the applicant’s personal details: Rank/Position/Salary and purpose of travel to the Philippines (In English);
7. Photocopy of Saudi Exit and Re-entry Visa;
8. Photocopy of Saudi Identification Card;
9. Confirm flight booking/details indicating onward destination after the Philippines;
10. Hotel Reservation or Letter of Invitation/Notarized Affidavit from host/sponsor in the Philippines;
11. Bank statement;
12. Police Clearance; ..........