He says here that D7 is the fifth chord in the key of G. Still in most songs and places, you'll see D being used instead of D7 along with G.
D is the triad on the 5th note of the key of G. D7 adds the 7th. Both act as dominants and contain the leading tone that pulls back to the tonic chord. However, the added 7th makes that pull stronger since, in addition to the leading tone, it creates a tritone between the 7th and 3rd of the chord which contracts to the root and third of the tonic chord. Jazz uses 7th chords all the time, but the 7th chord may be too strong for use in the middle of a phrase in other types of music. The D chord is an essential part of a regular progression, but the D7 may be saved for strong or ending cadence points.
He actually uses both, D and D7 in the video. As a V chord, the two are usually interchangeable. Since he is using basic triads for most of the time, it makes sense to use D F# A on the D chord. Introducing the C to produce D7 makes it a 4 note chord, the only other one in this video being the F#m7b5, which isn't that common in pop type music.
Had he been consistent and used 4 note chords all through, they would be Imaj7, iim7, iiim7, IVmaj7, V7, vim7 and vii7b5. He didn't.
As already stated, D and D7 (in key G) are pretty well interchangeable, the 7 part resolving from note C to the major 3 of G (I). Resolution likes to move as little as possible, so that's a semitone. The other semitone move is F#>G.
Interesting, maybe, is that the C and the F# form a tritone, which is considered dissonant. Thus, needs to resolve, which it does, to a consonant major third.
'He says here that the fifth chord of G is D7' isn't totally accurate. He sometimes says it's D!