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ultisnips
UltiSnips - The ultimate snippet solution for Vim. Send pull requests to SirVer/ultisnips!
In that blog post that is done using the vim plugin vimtex, which gives you syntax highlighting, indentation, etc, and also provides a way of automatically compiling your latex code into a PDF.
Basically, you add vimtex as a plugin to vim, you configure it in your .vimrc file and specify things like which PDF viewer you want to use to view the output. In both the blog post and the github repo they use the PDF viewer zathura.
Snipets or code completion can be done in a number of different ways, and how that is configured will depend on what method you use. In the blog he uses the vim plugin ultisnips. You'll find details on configuration for that in that link.
The config is pretty symple, need something to navigate, something to autocomplete and something for tex, there are plenty of configs, but all of them shows vimtex as the playmaker for write latex with vim, for the autocompletion part you can use classics like youcompleteme, CoC or something pretty minimal like mucomplete, for snippets I highly recommend Ultisnips, pretty simple to configure, and pretty simple to write snippets, you can look in my vimtex configuration, my mucomplete config and my ultisnips config to have a complete suitable latex configuration, with this config you can write latex with ease and configure your latex using the shell-escape option to enable libraries like markdown or special functions for tikz and pgf. Good luck!