so this is a D major chord and the notes in that chord are: D, F# and A and it is shown properly

In the screenshot you attached:

string 6 (the fat one to keep it simple) is not played
string 5 is played open giving you an A note
string 4 is played open giving a D note
string 3 is played on the 2nd fret for an A note
string 2 is played on the 3rd fret for a D note
string 1 is played on the 2nd fret for an F# note

BTW, the way this chord is shown is not uncommon, the open A on the 5th string provides a fuller sound. This is entirely up to the music and your ears, many times people will not play the open A because they don't want the heavier sound, it really depends on how the song sounds best - so let your ears decide.

Bill

Edit: on the 2 "E" notes in standard tuning. We have the 2 E notes in standard tuning for reasons I don't understand other than if we didn't have them both - we would not have "standard tuning". There are many ways to tune a guitar and that is probably something you want to hold off on learning about till later on down the line, or until a song you are working on tells you to change the tuning. Until then don't worry about it.