This is in reference to the Slokha below (sloka link)
Shukla-Ambara-Dharam Vissnnum Shashi-Varnnam Catur-Bhujam | Prasanna-Vadanam Dhyaayet Sarva-Vighno[a-U]pashaantaye ||
Meaning: 1: (We Meditate) Who is Wearing White Clothes, Who is All-Pervading, Who is Bright in Appearance like the Moon and Who is Having Four Hands, 2: Who is Having a Compassionate and Gracious Face, Let us Meditate on Him To Ward of all Obstacles.
Why and How the slokha is attributed to Lord Ganesha?
In that Sloka the word Vishnum is in second case(dvitiya) implying Vishnu as the nama (actual undeclined noun). This name comes from the dhatu (verbal root) vish meaning all pervading. This attribute of all pervasiveness can only be truly applied to Vishnutattva. You will see in many places in Gita how Lord Krishna declares this all pervading nature of His.
One example is Gita 9.4:
By Me, in My unmanifested form, this entire universe is pervaded.
All beings are in Me, but I am not in them
While I do not know exactly why people attribute it to Lord Ganesha, long time ago I was under the impression that it was for Lord Ganesha for the same reason given by @jabahar. Lord Ganesha is generally worshiped before doing a religious activity in order to counteract any obstacles. Since this sloka has reference to the word vighna (obstacles) it is definitely a source of confusion to many. Ultimately Lord Ganesha gets his power to remove obstacles from Lord Krishna or Vishnu only.
Lord Krishna in Gita 7.22 states:
Endowed with such a faith, he endeavors to worship a particular demigod and obtains his desires.
But in actuality these benefits are bestowed by Me alone
In Brahma Samhita 5.50 Lord Brahma says.
yat-pada-pallava-yugam vinidhaya kumbha-
dvandve pranama-samaye sa ganadhirajah
vighnan vihantum alam asya jagat-trayasya
govindam adi-purusam tam aham bhajami
I adore the primeval Lord Govinda, whose lotus feet are always held by Ganesa
upon the pair of tumuli protruding from his elephant head in order to obtain power
for his function of destroying all the obstacles on the path of progress of the three worlds.
So, overall, the direct meaning refers only to Lord Vishnu and there is no need to go for indirect interpretations when the direct meaning is fully clear both from the nama (word Vishnu )and the attributes of all pervasiveness (Vish dhatu) and ultimate remover of obstacles (Vighnas).
This is actually a shloka that is attributed to Lord Vishnu, not Ganesha. The link you have provided also mentions it as a shloka for Vishnu.
However, it can also be attributed to Shri Ganesha, or rather, it can be confused as a shloka for Lord Ganesha due to the presence of the last word सर्वविघ्नोपशान्तये (all obstacles are appeased). It is actually Lord Ganesha who is known as the lord and remover of obstacles. So Ganesha is also known as Vighnesha (Vighna + Isha). So if the word Vishnu is taken literally as all pervading and emphasis is given to the last word regarding obstacles, one can also attribute it to Ganesha. But having said that, it is worth noting that it is actually a widely used shloka for Lord Vishnu, but not Lord Ganesha. Other qualities given in the shloka suite more to Vishnu rather than Ganesha.
One of the most famous sloka dedicated to God Ganesha is as follows...
Vakratunda mahaakaaya suryakoti samaprabhaa. Nirvighnam kurumedeva sarvakaaryeshu sarvadaa
Meaning
We salute the matchless Lord Ganesha, whose bended trunk (vakra-tunda) and monstrous form (maha-kaayaa) sparkles as a million suns (surya-koti) and showers his endowments on everybody (sama-prabhaa). Goodness my master of masters Ganesha (kurume-deva), generously uproot all impediments (nir-vighnam), dependably (sarva-) and eternity (sarvadaa-) from all my exercises and attempts (sarva-kaaryeshu).
Source: http://www.ishtadevata.com/blog/vakratunda-mahaakaaya.html
