"Playing to the gallery" means doing or saying things that will make people admire or support you, instead of dealing with the actual matters at hand. It's like being an actor on a stage - the politician says things that he thinks will please his audience, even if the things he says are not helpful in actually solving the problem.
Likewise "playing to the strategy" means that Mr. Zaid was not interested in actually helping his people, but rather to say things in public that would be pleasing to Umno - his comments supported the beliefs/policies/strategies of Umno.
The short explanation is that Mr. Zaid was trying to be popular, not helpful or effective.
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