Let's not confuse the "One Belt, One Road" strategy with an alliance system or mistaken it to be some political design. China envisions a trade and economic development strategy that links both ends of Eurasia where two of the three largest economies in the world reside. The belt and the road string together a host of developing countries in between where China sees trade and investment opportunities, leveraging its financial muscle, infrastructure development skills and overall development model.
Japan and Taiwan continue to be among China's largest trading partners, but they don't need China's financing and infrastructure building skills. There is no need to put them as stops along the "One Belt, One Road" - they have direct links with China. As for Philippine, they're off the belt and road, and is not particularly attractive as an investment destination or trading opportunity - what Philippine would trade with China for infrastructure investments? Banana? The fact that Philippine is politically hostile to China obviously does not help - but that in and of itself is not the barrier for trade and investment relationship. Think about Japan.
Of course, China will gain international influence if its belt-and-road strategy is successful, aside from reaping economic benefits. But that's a side benefit and is not what its strategy is based on.