I've never heard that this category must involve an infectious process - do you know where you received this information? 'Spondylopathy' is a very generic term that just mean a disorder of the vertebrae and does not imply an infectious process. 'Inflammatory' only means that there is inflammation, and this may or may not involve an infection.
The other conditions you list all have their own coding categories in ICD-10, so I'm not sure why you're asking if these would 'fall under' this category. DDD classifies to 'intervertebral disc disorders', usually in categories M50-M51; DJD classifies as spondylosis or ostearthritis, depending on the site and type; spinal stenosis has its own category, M48.0-; facet arthropathy does not have a specific code, but would generally take you to M12.88 - Other specific arthropathies, not elsewhere classified, other specified site - unless documentation gives you more information than this. Hope this helps a little?