Technically, they could be called dyads, but context matters.
But what others have said is correct. It's basically a harmonized melody, but you can imply fully harmony with less notes and you also have to keep in mind the role that the sustained notes play as part of the harmony.
On the first beat, you're still playing all 3 parts of an F major triad. Technically, all you need is the root and the 3rd. The 5th is optional. Using just the root and the 5th gives you a different type of chord that sounds neither major or minor, but the listen draws context from the music around it. These are often labeled as something like F5, and are the common "power chords" used in a lot of styles of music, especially with rock guitar.
As a general rule, with simple music, you can almost always safely harmonize a melody by playing the note a 6th below (the same as a 3rd above, but down the octave). Just keep the notes inside the key (or diatonic) and this will work, even for notes that are melodic passing tones (notes that aren't part of the chord).
In the first bar, , beats 1, 3, and 4 all have notes exclusively from the F major triad. However, the top note of the melody on beat 2 is a G, which isn't in the chord, but it is in the F major scale. It's just a passing tone, and using the 6th below it (a Bb in this case) still sounds pretty good in parallel motion to the melody.
Someone could argue that the notes in in the 2nd beat (including the whole note holding over from beat one) would make a Gm7/F, and while that's a legitimate chord in the key of F, it really doesn't make sense here. This is a problem with thinking of theory too mathematically and not enough in context. It doesn't function as a Gm7/F. The whole bar is obviously just melody material with a melody that is harmonized. Trust your ears for that sort of context.
As a general rule in simple music, you probably aren't changing chords that much if the bass isn't moving. An example from this piece where I think harmonic motion is more strongly implied is in the 5th bar.
On beat 2, you have a a C in the melody on the downbeat, as well as a G and Bb in the bass. With a little theory knowledge, context, and clues from your ears, you'll hear this as a Cdom7 chord even though it's missing the 3rd. It is the V chord in the key of F. In this case it's a C7/G. While it might seem like passing material on paper, our ear tells us that there is obvious harmonic motion from I-V-I.
EDITORIAL NOTE: Also, whoever wrote this made a very poor choice in measures 3 and 4. Even if you have large hands with a good reach, those chords in the right hand a nearly impossible. It would've made much more sense to put the A into the bass clef. If the argument is that that would be too complicated, it's way less complicated than putting a 10th with a 3rd on the thumb side of the hand.