Let's just say, then, an alternate form of Manichaeism (and which could be called by something else), as it was influenced by Buddhism and other Eastern religions (which would surely exist without Judaism) just as much as Judaism, Christianity, etc.
...that still makes 0 sense.
Its like saying an alternate form of Islam in a world where the Arabian peninsula has fallen beneath the waves.
But on the influence of Buddhism on Manichaeism... yes and no.
Much of the association between the two is of course there in early Manichaeism, but in more of a respectful way, and largely for pragmatic purposes. The advantage of Manichaeism on the silk road was that, like Buddhism, it was hyper inclusive and so in many ways HAD to be favourable towards Buddhism because it was the other inclusive alternative.*
Its theology and practice however for much of its earlier years was still fundamentally more akin to Abrahamic philosophy, adressing philosophical issues within the bible and having relevatory texts about biblical stories in a way akin to mormonism. This is further compounded by the nature of Mani as the "paraclete" or embodiment of the holy spirit as Christ was the embodiment of the son.
When it became forced east by the rise of Islam, it was there and then that it lost much of its abrahamic side and embraced Buddhidm wholesale.