καὶ κατὰ φθόνον οἴονται τὸν ἑαυτῶν λέγειν,
is this ton a demonstrative pronoun, or is it an article that belongs to phtonon?
It’s the latter, jealousy of themselves. (Demonstrative is out of the question.) It must be applying to each of them, i.e. each thinks that the other is speaking in jealousy of him, but thanks to the plurals this is collapsed to “they think that they’re speaking in jealousy, the (jealousy) of themselves.” Fleshed out by the following φιλονικοῦντας etc.