κερητίζειν: Ancient Greek Field Hockey?

A brief note for the Classicists still reading, despite the deluge of very very Late Greek here—to point to a post at Nikos Sarantakos' blog, jointly researched with commenter π2, on whether the infrequent verb κερητίζειν refers to an Ancient Greek sport similar to field hockey. This has been claimed by the archaeologist Georgios Oikonomos in the 1920s, and the claim is repeated by the Greek Hockey Association—along with an relief clearly showing a kind of hockey being played in antiquity.

[Oikonomos, G. "Κερητίζοντες." Archaiologikon Deltion 6 (1920-1921): 56 -59: pp 56 57 58 59]
The verb is very rare (Hesychius with an unclear gloss, Pseudo-Plutarch Lives of the Ten Orators 839c, where most editors emend it to κελητίσαι, κελητίζων "ride a horse": "He is said to have run a race on a swift horse"). Sarantakos and π2 are unconvinced by Oikonomos' argument. As often happens, someone makes a claim in scholarship, and it's taken up without much question elsewhere, because peer review does not catch everything—and didn't apply to everything either.

The post's executive summary, as they give it:

• Yes, the Ancients played ball games.
  
• There probably was a word κερητίζω, but we don't know what it means.
  
• There is a chance that κερητίζω means a ball game.
  
• G. Oikonomos conjectures that that ballgame is the ballgame shown in the relief. But it could be any ballgame, e.g. a kind of tennis or rugby.
  
• His conjecture is nonetheless accepted by most scholars of Ancient sport—though the the conjuncture is forced in his opinion.
  
• But the association's motto κερητίζειν ἐστι τὸ μετὰ τέρψεως ἀθλεύειν "playing hockey means having fun in sport" is not ancient: it is probably made up based on a general comment on ball games by Galen (de parvae pilae exercitio, Kühn vol. 5 p. 900): τοῦτο μὲν δὴ κοινὸν ἁπάντων γυμνασίων τῶν μετὰ τέρψεως, ἄλλα δ’ ἐξαίρετα τῶν διὰ τῆς σμικρᾶς σφαίρας, ἃ ἐγὼ νῦν ἐξηγήσομαι "that is what all fun exercises have in common; but there are other excellent exercises with a small ball, which I will now expound on."