I am curious whether the model requires a font to be installed. Does it also generate the glyphs for the text?

Yes, it generates the text without using a font. Same is true of other image models like ChatGPT Images and Gemini Nano Banana and Midjourney.

It's a proprietary model as a service - it doesn't require anything outside of a browser. But even when they released open-weight (the original Qwen-Image) it's a diffusion model and can't use custom font files.