Did you read/view any of the references?
I tend to cite everything so that you have direct access to the source material for reference in case the context isn't clear.
This is not a "mess of buzzwords." It's how we move beyond the limits of Moore's Law. A lot of smart people have been working on various aspects of this for a long time. It's a big deal because it's a big change in how we model data, write algorithms, and think about computation in general, from the design of low-level hardware all the way up the stack to application design. It will behoove you to understand the change that's coming because it's what's next, and it's already here.
Re: your question on "Why did someone write an entire paper about counting triangles?"
Prof Tim Davis wrote the paper. He is one of the world's leading experts on sparse matrix implementations, and after the GraphBLAS Steering Committee finalized the 1.0 spec, they asked him to create the reference C implementation. Triangle counting is a common graph algorithm so it provides a familiar reference point when illustrating and comparing the characteristics of an implementation. Dr. Davis presented the paper this week at the HPEC 2018 conference (http://www.ieee-hpec.org), and in the paper's abstract he articulates precisely why:
Graph algorithms via SuiteSparse:GraphBLAS: triangle counting and K-truss
Abstract — SuiteSparse:GraphBLAS is a full implementation of the GraphBLAS standard, which defines a set of sparse matrix operations on an extended algebra of semirings using an almost unlimited variety of operators and types. When applied to sparse adjacency matrices, these algebraic operations are equivalent to computations on graphs. GraphBLAS provides a powerful and expressive framework for creating graph algorithms based on the elegant mathematics of sparse matrix operations on a semiring. To illustrate GraphBLAS, two graph algorithms are constructed in GraphBLAS and compared with efficient implementations without GraphBLAS: triangle counting and constructing the ktruss of a graph.
http://faculty.cse.tamu.edu/davis/GraphBLAS/HPEC18/Davis_HPE...
Watch the RedisGraph video for a general overview of how it works, but the big picture in the gist of it all is that data used in machine learning, AI, and relational databases is now being modeled in the same way -- as vectors/matrices/tensors -- to take advantage of modern CPU/GPU/TPU hardware accelerators that are being optimized for vector/matrix/tensor multiply-add operations. This means we can now run local and global algorithms in the same way, using the same code and the same data model, and we can return queries in real time -- executed in parallel, both locally or distributed -- it doesn't matter how the data is partitioned, the computation model is the same. Not only is this fast and compact, it unifies and simplifies things.