That article does not seem to say "every chord in a chord progression is always three notes...." The article is talking about triadic harmony; you can spell chords by taking every other note from a scale, but you can take four, five, six, or even seven notes. Further, you can add notes willy-nilly (more-or-less) to the fundamental triads.
Any collection of three or more notes is a chord, but not all chords have traditional names; some chords don't even have unique names. A set of notes that constitutes an Am6 may also be seen as an F#m7b5, depending on how you look at it. Note that some people (those people are wrong ;)) will call two notes a chord, but two notes can serve a very large number of distinctly different chords, which is to say, two notes alone can't establish any chord (although, frankly, neither can three notes, so the point may be splitting hairs).
A C chord is always C-E-G, and this can always function as a I chord in the key of C Major, but you could add other notes and still have a chord that functions as the tonic in C Major. For example, CMaj7: C-E-G-B, or CMaj9: C-E-G-B-D, or Cadd9: C-E-G-D, or C6: C-E-G-A, or CMaj13: C-E-G-B-D-F-A (probably played C-E-B-A on a guitar, or even a piano often enough) could all function as I chords in C Major.
The chord C-G-B might be used in place of a C chord, as a substitute, or especially if another instrument is holding down the E so that a complete CMaj7 chord is implied, but by itself C-G-B is not a C chord.
Typically, roman numeral notation is only used to specify the function of a chord, not the specifics of its voicing (the way the the notes are arranged). But you might sometimes see something like I7 or V7 for seventh chords to indicate that these aren't simple triads. In the key of C this may mean a CMaj7 and a G7, but occasionally someone will write IMaj7 to make it explicit that the C is a major 7th chord instead of a dominant 7th chord. If you come across roman numeral notation for a blues, you might find something like I7 - IV7 - V7, where the 7s indicate all dominant 7th chords. On the other hand, you might see a V in a roman numeral analysis of a piece of music, where the V represents not a G, but a G7 (in the key of C). In jazz it is pretty common to see ii - V - I, ii7 - V7 - I, IIm7 - V7 - I, or some combination of those symbols used to represent a Dm7 - G7 - CMaj7, or even some variation of that progression (e.g., Dm9 - G7#5 - CMaj9). In practice, the notation is a little bit all-over-the-map, so you have to be vigilant and aware of the context.
The best way to avoid (too much) confusion is to avoid learning your music theory from some website aimed at beginner guitar players, and instead to get a good music theory book to learn from. Or find a good teacher. That may be a little strong; you can learn useful bits of theory from websites like the one linked, just don't take the information gleaned from them as complete.