Even assuming attha.m could be equated to attā, it could not mean "the not taking as self", because gama here means"the going", so it would mean something like "the going to self of pain and sadness".
Also atthaṅgama is a common enough word to leave very little doubt over its meaning:
“yato kho, bhikkhave, bhikkhu channaṃ phassāyatanānaṃ samudayañca atthaṅgamañca..."
"iti rūpassa samudayo, iti rūpassa atthaṅgamo..."
“santāvuso, sattā sabbaso rūpasaññānaṃ samatikkamā paṭighasaññānaṃ atthaṅgamā..."
"ye hi keci, bhikkhave, samaṇā vā brāhmaṇā vā imāsaṃ dvinnaṃ diṭṭhīnaṃ samudayañca atthaṅgamañca..."
“puna caparaṃ, brāhmaṇa, bhikkhu sukhassa ca pahānā dukkhassa ca pahānā pubbeva somanassadomanassānaṃ atthaṅgamā adukkhamasukhaṃ upekkhāsatipārisuddhiṃ catutthaṃ jhānaṃ upasampajja viharati."
"yo tassā nirodho vūpasamo atthaṅgamo..."
The entire PED section on Attha 2 is of interest:
Attha2 (nt.) [Vedic asta, of uncertain etym.] home, primarily as place of rest & shelter, but in P. phraseology abstracted from the "going home", i. e. setting of the sun, as disappearance going out of existence, annihilation, extinction Only in acc. and as ˚ -- in foll phrases: atthangacchati to disappear, to go out of existence, to vanish Dh 226 (= vināsaŋ natthibhāvaŋ gacchati DhA iii.324), 384 ( parikkhayaŋ gacchati); pp. atthangata gone home, gone to rest, gone, disappeared; of the sun (= set): J i.175 (atthangate suriye at sunset); PvA 55 (id.) 216 (anatthangate s. before sunset) fig. Sn 472 (atthagata). 475 (id.) 1075 (= niruddha ucchinṇa vinaṭṭha anupādi -- sesāya nibbāna -- dhātuyā nibbuta); It 58; Dhs 1038; Vbh 195 -- atthagatatta (nt. abstr.) disappearance SnA 409. -- atthangama (atthagama passim) annihilation, disappearance opposed to samudaya (coming into existence) and synonymous with nirodha (destruction) D i.34, 37, 183; S iv.327; A iii.326; Ps ii.4, 6, 39; Pug 52; Dhs 165 265, 501, 579; Vbh 105. -- atthagamana (nt.) setting (of the sun) J i.101 (suriyass' atthagamanā at sunset DA i.95 (= ogamana). -- attha -- gāmin, in phrase udayɔ atthagāmin leading to birth and death (of paññā): see udaya. -- atthaŋ paleti = atthangacchati (fig.) Sn 1074 (= atthangameti nirujjhati Nd2 28). -- Also atthamita (pp. of i) set (of the sun) in phrase anatthamite suriye before sunset (with anatthangamite as v. l. at both pass. DhA i.86; iii.127. -- Cp. also abbhattha.
So no, that part of their translations seems fine.