Taylor Swift's song Wildest Dreams is in the key of A♭ major.
I'm not sure where you got those chords from, but I think the actual chords in the original album recording of this song are...
A♭ Fm E♭ Db
These chords all fit in to the key of A♭. However most of these chords don't really work as "open" shapes in a standard guitar tuning. With a capo on first fret you can play the following open chord shapes to get the correct chords sounding (as per the recording)...
G Em D C
This is a very common practice which simplifies chord charts which don't sit under the guitars "open" shapes.
If you want to play on piano you could use either set of chords, but if you want to play/sing along with the recording (or with a group of people playing "as recorded") you'll need to use the original chords.
I can't speak for other instruments or instrumentalists, but guitarists often talk in shapes but these shapes often don't refer to the sounding chord. I might say...
In that second bar play it as a D shape but up 2
...meaning, I want you to play an E chord but on the top 3 strings on frets 4 and 5.
You might want to look in to transposing chords and using a capo for more info.