Short answer. Yes — and so do you. Article 40 places the obligation on both sides: any alien seeking admission for employment purposes and any domestic or foreign employer who desires to engage an alien for employment in the Philippines shall obtain an employment permit from the Department of Labor.
What the law says
Any alien seeking admission to the Philippines for employment purposes and any domestic or foreign employer who desires to engage an alien for employment in the Philippines shall obtain an employment permit from the Department of Labor.
Labor Code, Article 40 — Work Permits For Foreigners. Read the full provision →
The duty runs to the employer as well
Read the sentence for who it names: Any alien seeking admission to the Philippines for employment purposes and any domestic or foreign employer who desires to engage an alien for employment in the Philippines shall obtain an employment permit from the Department of Labor. Employers routinely treat the permit as the foreigner's personal paperwork, something he arrives holding or does not. The provision does not read that way. It addresses the employer directly, and it reaches a foreign employer engaging someone for work in the Philippines just as it reaches a domestic one.
It is not a formality — there is a test behind it
The permit issues after a determination of the non-availability of a person in the Philippines who is competent, able and willing at the time of application to perform the services for which the alien is desired. That is a substantive condition, not a box to tick. The application is in effect a statement about the local labour market for one specific role, and the role as you have described it is what gets tested. Employers who write the post loosely and then explain the candidate's necessity afterwards make the harder version of this application for themselves.
Who the permit is aimed at
The article is headed as the employment permit of non-resident aliens, and it says the permit may be issued to a non-resident alien or to the applicant employer. So the question of whether your prospective hire is a resident or a non-resident alien is not incidental — it determines whether this provision is the one you are working under. If a recruiter or the candidate himself tells you the permit is unnecessary, that assertion is really a claim about his status, and it should be checked against his actual immigration papers rather than accepted.
One route that shortens the enquiry
For an enterprise registered in preferred areas of investments, the article says the permit may be issued upon recommendation of the government agency charged with the supervision of that registered enterprise. If your company holds such a registration, the supervising agency's recommendation is the practical path and is worth raising early. Whatever route applies, keep the job description, the recruitment record for the post, and the permit itself with the personnel file. Those are the documents that answer, later, why this particular foreigner was engaged.