Wikipedia claims that this is an acronym from earlier in its development which was later discontinued:
WotC was sufficiently convinced and contracted LLS to develop the
service, which was then known as Magic Online with Digital Objects
(MODO). Initially, the idea of charging for virtual goods, as opposed
to a subscription model with unlimited access, was greeted with
skepticism. Additionally, concerns were floated over how solid the
server and trading code would be; if exploits were found, the
entire economy could easily be destroyed. After a period of
beta-testing, the game became available to the general public in June
2002. The name was changed from MODO to its final commercial title, Magic: The Gathering Online (MTGO).
The game apparently gained some notoriety during its development under this name, which may have caused it to stick. It's likely that this is simply an affectionate hold-over nickname from a time when this old name was relevant.