Meinong for beginners

Encapsulating Meinong's theory of objects, Bill  writes,
Some objects exist and some do not. Thus horses exist while unicorns do not. Among the objects that do not exist, some subsist and some do not. Subsistents include properties, mathematical objects and states of affairs. Thus there are two modes of being, existence and subsistence. Spatiotemporal items exist while ideal/abstract objects subsist.
Now I appreciate that this is a very brief summary, but the first two sentences read rather strangely.  Is the second intended to illustrate the first?  Or is there an argument hidden in here:
Unicorns do not exist,
Unicorns are objects,
Ergo, Some objects do not exist.
And are we back to treating 'exists' as a predicate?  Or is 'object' to be interpreted more widely as 'object of thought', so that together the sentences say something like
We can think of horses and there are such things,
We can think of unicorns but there are no such things.
Ergo, Some things we can think about exist and some things we can think about do not.
Is this problematic?  Is this what Bill's summary means? And is that what Meinong was saying?

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