This verse is given as an example by the author King Bhoja (aka Bhojadeva) in his rather encyclopedic ~11th-century work Sarasvatī-kaṇṭhābharaṇa, among (many!) other examples of word-play, specifically under the category or varṇa-citra (roughly, verses interesting because of the letters in them), under the broader umbrella of citra-kāvya ("stunning poetry"; constrained writing and other kind of stuff Oulipo might be interested in).
It occurs in the second pariccheda (~chapter) of the work. An edition of this work, with the commentary of Rāmsinha (on I–III) and of Jagaddhara (on IV) was published in the Kāvyamālā series of the Nirṇaya Sāgar Press in 1934 (second edition), edited by Paṇḍit Kedārnāth Śarmā and Wāsudev Laxmaṇ Śāstrī Paṇśīkar. There is a scan of this book available online (45 MiB PDF here), in which it occurs on page 267 (२६७, page 360 of the PDF). Here is the relevant part:
This same edition has also been transcribed and put online at SARIT, where you can see this verse and commentary. (Here's a view of the xml source based on (probably) an old fork of the official GitHub repo.) Here's their transcription of the above image (I fixed a couple of obvious OCR-like typos):
‘कः खगौघाङचिच्छौजा झाञ्ज्ञोऽटौठीडडण्ढणः ।
तथोदधीन्पफर्बाभीर्मयोऽरिल्वाशिषां सहः ॥ २६३ ॥’
क्रमस्थेति । वर्णसमाम्नाये येन क्रमेण कादयो मावसानाः पठितास्तेन क्रमेण व्यञ्जननिवेशः । कः खगौघस्तत्तत्प्रसिद्धावदानपक्षिसमूहस्तमञ्चतीति क्विनि संयोगान्तलोपे कृते च खगौघाङिति रूपम् । चितं संविदं छ्यति छिनत्तीति चिच्छं यदोजस्तन्नास्ति यस्यासावचिच्छौजाः । ‘झमु अदने’ अस्मात् क्विप् । ‘अनुनासिकस्य क्विझलोः ६।४।१६’ इत्युपधादीर्घः । ‘मो नो धातोः ८।२।६४’ इति नकार इति झान् परबलभक्षको ज्ञः पण्डितः । ‘स्तो श्चुना श्चुः ८।४।४०’ इति नकारस्य ञकाराः । अटाः सङ्ग्रामाङ्गणपर्यटनशीलाः सुभटास्तानोठते बाधत इति क्विप् । ‘उठ गतौ’ इति धातो रूपम् । तेषामीडीश्वरः । अडण्ढणोऽचपलः । डण्ढण इत्यव्युत्पन्नं चपलवाचि प्रातिपदिकम् । तथा अभीर्भयरहितः एवंविधः को नामायमुदधीन् पफर्ब पूरयामासेति प्रश्नः । उत्तरम्—अरीन् लुनन्ति या आशिषस्तासां सहः क्षमो मयो दैत्यराज इति ॥
I am tolerably fluent in elementary Sanskrit, so although I cannot claim to understand all the Pāṇinean derivations perfectly, I can tell you what the commentary says, with help from the source you linked and from this blog post. The commentary, like typical Sanskrit commentary, goes over the original almost word-by-word, interspersing meanings and explaining difficult/unusual words by giving their derivation using sūtras (from the grammatical system of Pāṇini's Aṣṭādhyāyī). So, I transliterated the above and split the sandhi-s, and added some typographical niceties (split the sentences into a bulleted list by which word is being explained):
‘kaḥ khagaughāṅ acicchaujāḥ jhān jñaḥ aṭauṭhīḍ aḍaṇḍhaṇaḥ |
tathā udadhīn papharba abhīḥ mayo arilvā āśiṣāṃ sahaḥ || 263 ||’
kramastha iti | varṇa-samāmnāye yena krameṇa ka-ādayaḥ ma-avasānāḥ paṭhitāḥ tena krameṇa vyañjana-niveśaḥ |
- [कः] kaḥ
- [खगौघाङ्] khagaughaḥ tat-tat-prasiddha-avadāna-pakṣi-samūhaḥ tam añcati iti kvini saṃyogānta-lope kṛte ca khagaughāṅ iti rūpam |
- [अचिच्छौजाः] citaṃ saṃvidaṃ chyati chinatti iti cicchaṃ yad ojaḥ tan-nāsti yasya asau acicchaujāḥ |
- [झान्] ‘jhamu adane’ asmāt kvip | ‘anunāsikasya kvijhaloḥ 6|4|16’ iti upadhā-dīrghaḥ | ‘mo no dhātoḥ 8|2|64’ iti nakāra iti jhān para-bala-bhakṣakaḥ
- [ज्ञः] jñaḥ paṇḍitaḥ | ‘sto ścunā ścuḥ 8|4|40’ iti nakārasya ñakārāḥ |
- [अटौठीड्] aṭāḥ saṅgrāma-aṅgaṇa-paryaṭana-śīlāḥ su-bhaṭāḥ tān oṭhate bādhate iti kvip | ‘uṭha gatau’ iti dhāto rūpam | teṣām īḍ īśvaraḥ |
- [अडण्ढणः] aḍaṇḍhaṇaḥ acapalaḥ | ḍaṇḍhaṇa iti a-vyutpannaṃ capala-vāci prātipadikam |
- [तथा] tathā
- [अभीः] abhīḥ bhaya-rahitaḥ
evaṃ-vidhaḥ ko nāma ayam
- [उदधीन्] udadhīn
- [पफर्ब] papharba pūrayāmāsa
iti praśnaḥ |
- [अरिल्वा] arīn lunanti yāḥ
- [आशिषां] āśiṣaḥ tāsāṃ
- [सहः] sahaḥ kṣamaḥ
mayaḥ daitya-rājaḥ iti ||
(The numbers you see above are references to Pāṇini, so that those who are expert in the vyākaraṇa tradition of grammar/derivation can “check the work” and arrive at those words by themselves.)
To translate into English, these are the words of the Sanskrit verse, in sequence:
kaḥ कः — means “who” (very common pronoun, obviously)
khagaughāṅ खगौघाङ् — here, "khaga" is a common word meaning "bird", "khagaugha" is a natural compound meaning "a flock of birds", from which the form "khagaughāṅ" meaning "one who makes (assembles) a flock of birds"
acicchaujāḥ अचिच्छौजाः — here, "cit" is a common word meaning "mind", "cicchaṃ" means the splitting/dividing/destruction of the mind, "ojas" is a common word meaning "strength/energy", and so अचिच्छौजाः means "one whose mental energies are not split/destroyed"
jhān झान् — from the verbal root √jham, "eating", and some sūtras, jhān is explained as para-bala-bhakṣakaḥ, "consumer (of the strength of others)"
jñaḥ ज्ञः — needs no explanation; common word meaning "one who knows", i.e., "scholar" or "expert" (perhaps more familiar from compounds like sarvajñaḥ, "one who knows everything")
aṭauṭhīḍ अटौठीड् — aṭa, wanderer (in the battlefield) + √uṭh, strike, slay + īḍ, master. "One who is master of (or, praised by) those who strike the wanderers (in the battlefield)"
a-ḍaṇḍhaṇaḥ अ-डण्ढणः — meaning given as "not fickle", thus "steadfast". (This word I couldn't find in a dictionary.)
tathā तथा — very common word meaning "thus" (or "and")
udadhīn उदधीन् — accusative plural of udadhi, ocean. Thus, "oceans" (in accusative case)
papharba पफर्ब — "filled". This is in the perfect tense, hence the reduplication (as in dadarśa, “saw”; compare Greek dedorka)
abhīḥ अभीः — common word meaning “fearless”
Mayaḥ मयः — a name! Maya.
arilvā अरिल्वा — from "ari" enemy + √lū “cutting/destroying”, meaning "foe-destroying"
āśiṣāṃ आशिषां — genitive plural of āśis, blessing
sahaḥ सहः — able to bear, worthy of bearing.
Some of those words are common words, some are common morphemes put together in either standard or unusual (but grammatical) ways, and only a couple are obscure lexicographically, but the verse is grammatical and translates roughly to:
“Who is he, who
assembles flocks of birds,
has his mental energies intact,
consumes the strength of others,
is a scholar,
is the lord of those who slay wanderers,
and, without fear, filled the oceans?
He is Maya,
worthy of blessings that destroy enemies.”
And putting the words together with the usual rules of sandhi, you get the verse in question.