Ya, neither song is a triplet. That synth line is just not playing all of the 1/8th notes but it is straight 4/4 time
Rawhide is 2/4 time common with C&W and Bluegrass.
Triplets are found in a lot of R&B, Blues, 6/8 time and 3/4 time stuff my teacher gave me an easy to remember count- you go
TRI_PL_LET it's like counting 3 four times per measure 123-123-123-123 ..
That's a very simplified explaination as most song won't use it like that.
Like the snare roll in you ain't nothing but a Houndog.
Country swing and songs like Rock around the Clock,, Triplets give music swing.
Often you'll play a part and quantize to 1/8th notes and it just plain sounds all wrong.
So try the 1/8th Triplet and see if it make it right.