The article you've linked to explains that Taiwan makes nearly the same claims as the PRC in the South China Sea.
In fact, the famous "dashed-line" claims in the South China Sea were originally made by the Republic of China, before it was defeated by the Communists. This is a map from 1947, showing the ROC's eleven-dash line: [0].
The only difference that I know of between the claims of the ROC and the PRC is that the PRC has slightly reduced its claims as a result of an agreement with Vietnam over the naval boundary in the Gulf of Tonkin.
> Taiwan makes nearly the same claims as the PRC in the South China Sea
Taiwan doesn’t assert the claim [1]. There is sensitivity around explicitly abandoning it, as “changing the ROC’s historical claims would indicate—especially to Beijing—that the island democracy was abandoning its historical political identity and moving towards an inherently Taiwanese national identity, or even independence” [2]. To the degree Taipei has legitimately aligned with Beijing, it has been in the limited sense of arguing Taiwan is legally a real island, not an islet which cannot make any maritime claims [3][4].
Taiwan not only asserts the claim, but actually occupies much more valuable islands than the PRC does. Like the PRC, Taiwan rejected the Philippines' claims and refused to recognize the arbitration body's decision or legitimacy.
Tsai Ing-Wen doesn't want to look like she's aligning herself with China on this issue, but this is long-standing ROC policy, going back to before the PRC was even founded. It's not something the PRC invented.
