Downloading/rendering rasterized tiles with custom Mapbox Style

Hi there!

I am developing a video game which uses satellite data to render terrain. I’d like to use OSM data to provide a base query for terrain features (such as where there are trees or buildings/cities). To do this, I’ve created my own Mapbox style, which outputs certain features (structures, foliage, water, roads) as easy to mask out colors, and I’d like to render this as offline textures. I’m a little confused as how I would actually go about doing this however.
The API I’ve been using is able to download Mapnik (plus some others) tiles via query in the format “{zoom}/{x}/{y}.png”. I can easily extract out the zoom+coordinates from that, but how can I turn this into a query using my own render style? Am I correct in assuming I’ll have to download the planet data and host my own tile server?

Thanks for your time!