The postcard shows the Parian Gate and the dome of one of the churches inside the walled city. I was browsing the book Ciudad Murada by Jose Victor Z. Torres when I came across on page 43 a similar picture showing Parian Gate or Puerta del Parian, the dome of Hospital de San Juan de Dios chapel and the rectangular cupola of Nuestra Señora de los Angeles known as the San Francisco Church.
I believe a lot of people do not know that there were actually 8 churches inside pre-war Intramuros (and there were also chapels). Some are more familiar with the Manila Cathedral dome. The cathedral is located near Fort Santiago, while the Puerta del Parian is at the northeast of Intramuros. Below is the map showing the location of Puerta del Parian.
#26 San Francisco Church and Convent
#27 Capilla de la Orden Tercera
#28 Hospital de San Juan de Dios
Here is another picture of the dome of Hospital de San Juan de Dios chapel and the rectangular cupola of the San Francisco Church.
Parian Gate Postcard
UPDATE: Parian Gate Postcard
Map from Ciudad Murada: A Walk Through Historic Intramuros
by Jose Victor Z. Torres
Hospital de San Juan de Dios, Manila 1897, Retrato: Filipinas Collection Thread 3