Many depends on voting system.
If there will be proportional elections with a threshold on a global level, then we, of course, won't see Zionist Party, Juche Party and most probably even a Shi'a party (Shi'a Muslims make up at best 2-3 % of the world population, they are divided internally and not all of them would vote along religious lines). Latin American leftists will probably either unite with social democrats or form a worldwide coalition of reformed communists and democratic socialists. Greens could join social democrats or split between social democratic, democratic socialist and liberal coalitions. Only India and China could afford to have national parties running in global elections without being a part of any international party/coalition.
If there will be proportional elections on national level without a global threshold (like the EU parliamentary elections) or any kind of majoritarian elections, then already existing parties will continue to run the show (of course, political landscape will change drastically in a countries where there are no currently free competitive multi-party elections, though in many of them currently ruling party would still have a good chance to obtain majority of seats), and in the parliament most of them will form very loose coalitions, probably along the already existing
internationals. Regional factor would be big as well: e. g. while many African parties will formally join Socialist or Liberal International, most of them could at the same time form a pan-African group, and division between developing and developed world (or, more likely, more developed and less developed parts of developing world, since developing world would dominate the world parliament due to it's huge population size) probably will be more significant in most cases than ideological differences (especially taking into account how many parties only nominally belong to their declared ideology). But while there will be quite a few of international coalitions of various kinds, it will take a lot of time until a truly worldwide parties (rather than a loose groupings of national parties) will emerge. Even in the EU, national parties still play more important role than pan-European ones.
Speaking about your list of possible parties: some of them will be too insignificant to worth mention, while at the same time you forgot about Christian democratic / conservative party similar to European People's Party which would unite major centre-right parties in Europe and possibly other parts of the world (the USA, Canada, Latin America etc.).
Maoist Party (far-left): Basically the "China party," and not necessarily trying to speak for all Maoists, but rather trying to promote the Chinese agenda.
Though Communist Party of China could try to form some kind of global coalition, Maoists (except CPC itself which is now Maoist in name only) are too weak, and most of them seem to prefer guerilla warfare to participation in legal elections... and I'm curious how many Maoists in the world outside China still view China as a Communist state? More likely, CPC will try to join The United Left (AFAIK Vietnam is as capitalist as China, so if The United Left accepts Vietnamese Communists, they should accept Chinese ones too).
Indigenous People's Party (left-wing): Supports indigenous people around the world, anti-colonialist.
Most of the indigenous peoples are either too small to form even remotely significant voting bloc, or already have their own independent state (so they don't need any anti-colonialism), or don't express desire to have a party that represents specifically their interests, and they are very different culturally and sometimes have contradicting interests... though there probably could be an alliance of separatist movements (similar to the already existing Unrepresented Nations and Peoples Organization) and it could also include some non-separatist ethnic or regionalist movements.
People's Congress (big tent): India's counterweight to China, no coherent ideology beyond promoting Indian interests.
Zionist Party (big tent): Meant to be the party for Jews around the world, but support is largely concentrated in Israel.
So you think that in India and Israel most of the significant parties will merge into one? Why? Even if this will happen, an opposition to this dominant party will emerge very soon, and after a several elections voters will become tired of the ruling party and opposition will win... In fact, India already was a dominant-party state before the 70s, so the story can repeat itself there. More likely, India and Israel would stay with roughly the same parties as now, though, of course, most of them will have the same or very similar position on many issues affecting Indian or Israeli national interests. Depending on the electoral system, there could be a single Zionist list running outside of Israel to attract some of the Jewish diaspora votes, but even this is unlikely.
Juche Party (left-wing): North Korea's party
By the way, how many people would vote for these guys in a free multi-party elections? In China and many other authoritarian regimes the ruling party is popular and have a good chance to gather majority of votes, but we can only guess what will happen in NK after it's unprecedented information isolation will be lifted or at least after people will be allowed to form opposition parties and freely criticize government (which is a prerequisite for a competitive election). Even if NK will become as democratic as China now, it will be a huge change with unpredictable and probably catastrophic outcome for the Kim dynasty (and, very likely, the entire country too). So I doubt there will be a "Juche party" at all. Though, maybe, the Workers' Party of Korea will survive, reform itself and expel the most odious members; in that case it could re-brand itself as a communist or social democratic party, or abandon socialism entirely and pose itself just as a Korean nationalist party.
Qutbist Party (right-wing): Party for far-right Islamists
How exactly far-right? To the extent of ISIS? Looking at al-Qaeda and ISIS currently fighting each other in Syria, I'm not sure they could form a single party (even if we assume they will be allowed to run in the elections). Though, maybe, you meant less extreme Islamists, like Egyptian al-Nour. Well, there will probably be enough room between your Islamic Justice Party and ISIS for such party.
