TLDR: If someone doesn't specific, go based off of what the tonic chord is major or minor.
First of the person in the video should not have called the one chord Eb. There are concepts in music called enharmonic equivalence where the same notes can have multiple names. Because we are looking at a key with a lot of sharps either way, calling the chord Eb doesn't make sense so it should be D# instead. Same goes for F which is actually an E#. Other sites for this show song in Db which is fine, but has all the chords written out with that in mind so you see chords that would appear in that key and never one with a sharp name.
Chords can be major or minor and I highly dout that you are playing only major keys based on the other site's version of this song. The quality of the chords will help define what is more appropriate to call the key as just a simple test can be checking whether the tonic chord is major or minor. Most of the time this is as far as you have to look to determine if the key. Also typical if it's in a major key you'll typically leave out the "major" when saying the key as major keys are typically more prevalent then minor keys.
This song starts on a C# major chord and uses the typical major chord of vi-IV-V (A#m - F# - G#) so the key is easily seen as C# major. This piece does modulate up the circle of 5ths however which is why the other site puts this in the key of Db as you'll start to get into double sharp territory if you start on C#.