That song is definitely in G major. The anacrucis at the start leads straight to a G in the first full bar. (1st clue). The last note - even though it looks odd, it must be a note due to wording underneath- is also G. (2nd clue). There are no D#s which would indicate not Em, due to most songs in Em needing and having a sharpened leading note, D# in Em (3rd clue).The repeated first line also ends on G (4th clue). There is no doubt here.
However - were there D#s it could easily have been in Em. The main clue there being ending on E. It could also have been in several different modes of G major, with F# as key sig., but clues would be tonal centre. For example, if the tonal centre (home feeling) was A, then it could have been A Dorian.