Both kanji take the kun'yomi here. For 物, that's もの, which you learned with the vocabulary 物. You learned the kun'yomi for 語 with the verb 語る, but here it becomes がたり because of rendaku, and the り is tucked inside the kanji.
Maybe you've already heard the word ものがたり too. It's in some film and book names. If you haven't, and you find this reading hard to remember, think of a story about an infamous Gatling (がたり) gun that wandered the land, mowing everything down in its path. It's a terrible legend, but what if it were true???
I think she's acting like she's the main character of a story.
The Tale of the Bamboo Cutter is a famous Japanese legend.
I’m writing a story right now. It’s about a sad guy who is obsessed with puppies.