Usually React+Redux project min + gz will come in around 200-300KB for a relatively simple app... If you go with preact, and are really judicious in what you bring in, you can hit half that. For most people, if your initial send is under 500kb, it won't be noticed except some mobile connections.
YMMV of course, for comparison, angular apps tend to be about 50-80% bigger, and ng2 apps over twice the size. At least from my own experience and setting up a few boilerplate apps.
What stuff are you bringing in? Preact is 3kb, Redux + bindings for Preact probably bring it around 10kb or less (compressed). Unless you mean images and stuff.
The author either didn't do the best choice in writing his page, or has great plans for it.
[1] https://webpack.github.io/docs/configuration.html#devtool
Even if compressed and minified, that's still a huge amount of JS statements that the interpreter has to go through.
I'm getting about 2 seconds to DomContentLoaded on my iMac and a reasonably fast cable connection. Four seconds to visible content on my Nexus 5X on same connection.
This is the kind of crap that makes the web feel so lame and clunky on mobile (and on desktops too even sometimes).
Then again, Immutable.js is about 15kb on it's own, and a few other heavy hitters and you'll hit 100kb (gz) load before much functionality. That said, I think a 500kb target for a web app isn't too bad, this does exceed that, but not sure if certain bits (image references, fonts, etc) are part of the actual JS bundle, which will bloat it out a lot.
Often times you will wind up with competing libraries that both get installed... You'll get all of lodash, and all of Ramda... you'll get all of jQuery, and a few other tools because you're bringing in one component. Working on larger applications with people less judicious as to what they bring in results in a lot of bloat... more so when it's easier to bring something in (thanks to webpack/babel), and while I appreciate that, it's a tool that's easy to abuse.
In the end, you can get react+redux in under 100kb, you can get a lot of the app boilerplate for a mid-sized app well under 200kb... I would compare this to angular, or ng2 that tend to be much bigger. In the end it's how you are building.
Beyond this, as I said, I didn't really look into the bundle... depending on configuration it could be including images, fonts and css. Which would mean it's really not that bad, though it should probably be using url-loader for a lot of the assets to break into separate downloads. Also, react-icons is much better when only needing a few icons from the libraries, they're also well normalized to mix/match in terms of size/position than the fonts tend to be.
While 700 Kb is sort-of-acceptable in terms of data usage, the execution of 2.8 Mb of JS is quite taxing on the browser: on my 2010 MacBook Pro it takes 4-5 seconds to show the text on the page, even when bundle.js is cached...