The nature of graffiti, typically an ephemeral art form, makes it difficult to ascribe authorship. I did some snooping around, and the means by which people date and identify graffiti often yields wide date ranges. Identifying a specific author and time appears nearly impossible. One article I glanced at that dealt with graffiti in a Hospitaller preceptory in north-eastern Spain gave date ranges of over a hundred and fifty years.

This particular example comes from Chinon and its expansive chateau complex. Chinon, straddling the Vienne river as it does, proved to be an important vantage for anyone seeking to exercise control upon the Loire in the Middle Ages and beyond. As such, it is hardly surprising that it both occasionally functioned as a royal residence and a place to hold hostages. Besides the famous imprisonment of the Templars, I wouldn't be surprised if persons were held there also during the later phases of the Hundred Years War, when Charles VII took frequent residence there and expanded some of the structures.

All of this is to say, I am unsure if the authorship is from Templar prisoners, but I would advise caution in this area, particularly given the website from which you linked the image. The graffiti, while cool, doesn't resonate as particularly anything unique within the pantheon of weird medieval graffiti. For example, there is the so-called crusader graffiti at the Holy Sepulcre that shows similar themes. I am not aware historian of either the Templars or Chinon itself who specifically ascribes this example of graffiti to the Templars during their stay, although some of it probably did happen then.

For the mentioned chapter on Hospitaller graffiti, see Gerrard & Dauber, "Building Biographies: Graffiti, Architecture and People at the Hospitaller Preceptory at Ambel (Zaragoza), Spain" in the Military Orders Vol. 4 (2008).

edit: sentence structure requires that I, on occasion, employ a verb.