Rev. 7:12 λέγοντες· ἀμήν, ἡ εὐλογία καὶ ἡ δόξα καὶ ἡ σοφία καὶ ἡ
εὐχαριστία καὶ ἡ τιμὴ καὶ ἡ δύναμις καὶ ἡ ἰσχὺς τῷ θεῷ ἡμῶν εἰς τοὺς
αἰῶνας τῶν αἰώνων· ἀμήν.
Rev. 7:14 καὶ εἴρηκα αὐτῷ· κύριέ μου, σὺ οἶδας. καὶ εἶπέν μοι· οὗτοί
εἰσιν οἱ ἐρχόμενοι ἐκ τῆς θλίψεως τῆς μεγάλης καὶ ἔπλυναν τὰς στολὰς
αὐτῶν καὶ ἐλεύκαναν αὐτὰς ἐν τῷ αἵματι τοῦ ἀρνίου.
οὗτοί εἰσιν οἱ ἐρχόμενοι ἐκ τῆς θλίψεως τῆς μεγάλης
The articular participle οἱ ἐρχόμενοι is found in a this is that clause οὗτοί εἰσιν οἱ ἐρχόμενοι "these are the ones coming. ἐρχόμενοι followed by ἐκ with the genitive marks a movement "out from" an event τῆς θλίψεως τῆς μεγάλης the great tribulation.
In the Apocalypse, John uses ἐκ with the genitive frequently. Take a look at Rev. 16:13.
Rev. 16:13 Καὶ εἶδον ἐκ τοῦ στόματος τοῦ δράκοντος καὶ ἐκ τοῦ
στόματος τοῦ θηρίου καὶ ἐκ τοῦ στόματος τοῦ ψευδοπροφή του πνεύματα
τρία ἀκάθαρτα ὡς βάτραχοι·
And I saw [coming] out of the mouth of the dragon and out of the
mouth of the beast and out of the mouth of the false prophet, three
unclean spirits like frogs;
Both the Apocalypse and John's Gospel show frequent use of ἐκ with the genitive. Compared to the synoptic Gospels John stands out in this regard.
In regard to the Ancient Greek Article:
It it is both similar and distinct from the English Article. Intro courses often stress the similarities. Long term students of the language will find out how important it is to become familiar with the peculiarities.
Richard A. Hoyle, Scenarios, discourse and translation. SIL 2008