First off, as Sheldon Pollock points out in his translation of Ayodhyākāṇḍa, the two verses you quote in your question have been removed from the Critical Edition of Vālmīki Rāmāyaṇa.
1. In order to establish a reasonable transition between sargas, the SR [Southern Recension] inserts
before this verse four lines (2091*), in which Rāma, having shown Sītā around the
mountain, sits down on the slope and gives her cooked meat to eat (thus attempting
also to account for the fire mentioned in 87.21ff, and verse 10 below, cf. note on
89.19; it seems more likely that the fire is the one on the sacred altar, cf. 93.11 and
23, though whether one may unceremoniously douse a ritual fire, as Lakṣmaṇa will
suggest in verse 10 below, is questionable).
And even if those were present in the original Rāmāyaṇa, medhya and māṃsa together usually mean "fresh or pure meat" and not "pulp made out of fruits and roots":
tāṃ tathā darśayitvā tu maithilīṃ girinimnagām |
niṣasāda giriprasthe sītāṃ māṃsena candayan || 2-96-1
tathā = thus; darśayitvā = having shown; girinimnagām = the mountaneous river Mandakini; tāṃ sītāṃ = to that Seetha; maithilīṃ = the daughter of the king of Mithila; niṣasāda = sat; giriprasthe = on the hill side; candayan = in order to gratify her appetite; māṃsena = with flesh.
Having shown Mandakini River in that manner to Seetha, the daughter of Mithila, Rama set on the hill-side in order to gratify her appetite with a piece of flesh.
idaṃ medhyamidaṃ svādu niṣṭaptamidamagninā |
evamāste sa dharmātmā sītayā saha rāghavaḥ || 2-96-2
saha rāghavaḥ = that Rama; dharmātmā = of righteousness; āste = stayed; sītayā saha = with Seetha; evam = thus speaking; idaṃ = this meat; medhyam = is fresh; idaṃ = this; niṣṭaptam = was roasted; agninā = in the fire.
Rama, whose mind was devoted to righteousness stayed there with Seetha, saying; "This meat is fresh, this is savoury and roasted in the fire."
Translation served by valmiki.iitk.ac.in also uses similar meanings for those words:
मैथिलीम् princess of Mithila, तां सीताम् to Sita, तथा in that way, गिरिनिम्नगाम् mountainriver, दर्शयित्वा having shown, मांसेन with meat, छन्दयन् gratifying, गिरिप्रस्थे on the mountainslope, निषसाद sat.
Rama showed Sita, the princess of Mithila the river Mandakini flowing in the mountain, gratified her by offering meat (to eat) and sat on the mountain slope.
धर्मात्मा righteous, स राघवः that Rama, इदम् this, मेध्यम् sacred meat, इदम् this, स्वादु is savoury, इदम् this one, अग्निना with fire, निष्टप्तम् roasted, एवम् uttering this way, सीतया सह in the company of Sita, आस्ते was seated.
Offering Sita several kinds of preparations to eat, righteous Rama, seated in her company remarked, This meat is savoury, this meat roasted on fire is sacred.
Now, to answer your underlying question:
So now the question is why this particular translator chooses फल-मूलके गूदेसे (pulp made of fruits and roots)?
There are several commentaries/commentators of Vālmīki Rāmāyaṇa and one particular commentator, Vaṃśīdhara Śivasahāya, consistently uses fruits and roots instead of meat in his commentary, Śiromaṇi, abbrev. as Cr below.
- Cg: the commentary called Bhūsaṇa (the name of the commentary on Bālakāṇḍa is Maṇimañjīrā, on Ayodhyākāṇḍa is Pītāmbarā) of Govindarāja
- Ck: the commentary called the Amrtakataka of Kataka Mādhavā Yogīndra
- Cm: the commentary called Tattvadīpikā of Maheśvaratīrtha
- Cna: the commentary of Sarvajña Nārāyaṇa (as cited by Lokanātha Cakravarti)
- Cr: the commentary called Śiromaṇi of Bansidhara (Vaṃśīdhara) Śivasahāya
- Crā: the commentary of Rāmanuja
- Cs: the commentary of Satyatīrtha
- Ct: the commentary called Tilaka of Nāgeśa Bhaṭṭa, composed in the name of Rāmavarmā
- Ctr: the commentary called Dharmākūtam of Tryambaka Yajvan
- Ctś: the commentary called Taniślokī of Ātreya Ahobala
- Cv: the commentary called Vivekatilaka of Varadarāja Uḍāli (Uḍāri)
- Cmu: the commentary called Munibhāvaprakāśikā - author unknown.
And the Gita Press translation which you cite in your question appears to follow the Śiromaṇi commentary throughout. One possible reason why Gita Press used this commentary over others is, its founders (Jayadayal Goyandka and Hanumanprasad Poddar) wanted to promote vegetarianism in India and among Hindus.
To illustrate the extent Śivasahāya (Cr) goes to portray Rāma as a vegetarian prince, let's look at this verse:
tau tatra hatvā caturaḥ mahā mṛgān |
varāham ṛśyam pṛṣatam mahā rurum |
ādāya medhyam tvaritam bubhukṣitau|
vāsāya kāle yayatur vanaḥ patim || 2-52-102
Having hunted there four deer, namely Varaaha, Rishya, Prisata; and Mahaaruru (the four principal species of deer) and taking quickly the portions that were pure, being hungry as they were, Rama and Lakshmana reached a tree to take rest in the evening.
Now compare with Pollock's notes:
79. "meat" medhyam: This follows Ck, though the word is rarely used in this sense: alternatively, and perhaps preferably, we should read with T1, 2, G1, 3 medhyāṃs, "pure," that is, animals, those fit to consume; cf. 49.14, medhyān mṛgān, so in 50.16. In the NR substitution (1098*) the brothers kill only one beast (a dappled antelope), light a fire, cook, and along with Sita eat the meat, and then retire for the night beneath a tree.
Finally, and with a vengeance, Rāma breaks his fast (cf. note on 41.8 above), and
it is noteworthy that he does so by eating meat (cf. note on 17.15, and contrast his
words to Guha in 44.19-20, and to Bharadvāja in 48.15 [but see note ad loc.]). Ct
(similarly Ck) remarks, "Meat is included in 'forest fare,' there is no fault here;
nor is there any in his killing animals, since it is part of the dharma of hunting."
Cr's gloss displays an amusing perversity: "'He struck great animals,' that is, he
knocked them about in fun and then took 'pure' food, fruits, etc."
Once again the Gita Press translation follows Cr almost word for word:
वहाँ उन दोनों भाइयोंने मृगया-विनोदके लिये वराह, ऋश्य, पृषत् और महारुरु-इन चार महामृगोंपर बाणोंका प्रहार किया। तत्पश्चात् जब उन्हें भूख लगी, तब पवित्र कन्द-मूल आदि लेकर सायंकालके समय ठहरनेके लिये (वे सीताजीके साथ) एक वृक्षके नीचे चले गये ॥१०२॥