It was to those alive at the time. I agree.
But is there a reason to think He didn't also mean all descendants of Adam and Eve?
I believe Matthew 24 is talking about the generation of those living at the time because Matthew is consistent with the way that he uses the term generation throughout his Gospel.
Strong's Concordance
genea: race, family, generation
Original Word: γενεά, ᾶς, ἡ
Part of Speech: Noun, Feminine
Transliteration: genea
Phonetic Spelling: (ghen-eh-ah')
Definition: race, family, generation
Usage: a generation; if repeated twice or with another time word, practically indicates infinity of time.
Thayer's Greek Lexicon
STRONGS NT 1074: γενεά
3.
the whole multitude of men living at the same time: Matthew 24:34; Mark 13:30; Luke 1:48 (πᾶσαι αἱ γενεαί); ; Philippians 2:15; used especially of the Jewish race living at one and the same period:
Matthew 11:16; Matthew 12:39, 41f, 45; Matthew 16:4; Matthew 23:36; Mark 8:12, 38; Luke 11:29f, 32, 50; Luke 17:25; Acts 13:36; Hebrews 3:10; ἄνθρωποι τῆς γενεάς ταύτης, Luke 7:31; ἄνδρες τῆς γενεάς ταύτης, Luke 11:31; τήν δέ γενεάν αὐτοῦ τίς διηγήσεται, who can describe the wickedness of the present generation, Acts 8:33 (from Isaiah 53:8 the Sept.) (but cf. Meyer, at the passage).
4.
an age (i. e. the time ordinarily occupied by each successive generation), the space of from 30 to 33 years (Herodotus 2, 142, et al.; Heraclitus in Plutarch, def. orac. c. 11), or ὁ χρόνος, ἐν ᾧ γεννωντα παρέχει τόν ἐξ αὐτοῦ γεγεννημένον ὁ γεννησας (Plutarch, the passage cited); in the N. T. common in plural: Ephesians 3:5 (Winers Grammar, § 31, 9 a.; Buttmann, 186 (161)); παρῳχημέναις γενεαῖς in ages gone by, Acts 14:16; ἀπό τῶν γενεῶν for ages, since the generations began, Colossians 1:26; ἐκ γενεῶν ἀρχαίων from the generations of old, from ancient times down, Acts 15:21; εἰς γενεάς γενεῶν unto generations of generations, through all ages, forever (a phrase which assumes that the longer ages are made up of shorter; see αἰών, 1 a.): Luke 1:50 R L (דּורִים לְדור, Isaiah 51:8); εἰς γενεάς καί γενεάς unto generations and generations, ibid. T Tr WH equivalent to וָדור לְדור, Psalm 89:2; Isaiah 34:17; very often in the Sept.; (add, εἰς πάσας τάς γενεάς τοῦ αἰῶνος τῶν αἰώνων, Ephesians 3:21, cf. Ellicott at the passage) (γενεά is used of a century in Genesis 15:16, cf. Knobel at the passage, and on the senses of the word see the full remarks of Keim, iii. 206 (v. 245 English translation)).