Nope. Don’t use OSM for this - we’re not here to catalogue every single third-party identifier in the world, let alone proprietary ones with no evidence on the ground.
You can create your own map using a site such as umap.openstreetmap.fr; or build your own tool using leaflet.js or similar; or create a database that references OSM objects via wikidata identifiers.
I believe these places are generally not identifiable as such on the ground, without using the app. Is that correct? In that case, the answer is unfortuntately going to be: We cannot legally map those in OSM, as it would amount to (directly or indirectly) copying the official databse, which is property of Niantic.
The pokestops themselves are not.
However, the pokestops always represent some form of POI: a statue, a chapel, a mural, artsy grafiti, historic buildings, …
While you cannot add the stops, the POI’s that match are surveyable in the field and can (based on a survey) be added to OSM as whatever POI they are.
That said: there is little to no actualisation of the database: there’s quite a few ‘pokestops’ that represent items that have either moved or disappeared, that don’t get removed from the game if nobody reports them.