Hello N J. It would be good to know if in the app you can see any image to contextualize the sentence and have a visual point of reference. "Esto tiene trescientos años! Quiero una pintura más nueva. "Esto, este, esta" are deictics, which means that the gender is determined by de positions of the speakers with regard to the reference. Probably, "esto" in your sentence refers to a masculine noun we are not aware of (el carro, el cuarto, etc.) because we don't know the scenario of the speaker. In conclusion, you are right, you need to know the gender of the non for using grammatically correct the demonstratives adjectives "esto, esta, este" but you always need to identify the non the speaker is referring to. That's the main complaint I have with the language learning apps, they use isolated phrases. Hope it helps.

Hi N J! You're idea about the object's gender It's right but "¡Esto tiene trescientos años!" is a derogatory phrase (Frase despectiva), a little bit ofensive, in this case doesn't matter the gender. I hope this can be useful. Bye!