How do you play the notes in the red square? On the upper staff, the lower chord is G but the note in the lower section is also G. Do you just ignore it?
You are ignoring the dotted line with 8va written above the upper G-clef. This means that the notes written in this clef should be played an octave above the written notes. (This notation is called All'ottava and is sometimes used to avoid ledger lines.)
When you do this there is no conflict between the notes in the red box.
Well, "Jingle Bells" ain't no Bach, but the same principles apply: if you have two voices hogging one key, you play in a manner doing justice to both. In this case, the left hand has a leading voice down, so you strike the key hard enough (and possibly with the tiniest of lead which you keep up for the rest of the left-hand phrase) to have it distinguishable from the accompanying character of the B, but make sure to release it simultaneously with the B so that the mental afterimage is a release of a plain two-note "chord".
[Striking of the clue bat]
Now after answering your question with a nice treatment about doing two voices on one key justice, the music in question does not, in fact, have two voices on one key. That's because the upper staff is adorned with "8va-----" and thus to be played one octave higher than written in the staff.
No collision whatsoever. But the answer may still hold another time.
As pointed out by @Tim H, the 8va sign means the two hands are not in the same octave so there is no 'collison.'
But, keep in mind some keyboard music for harpsichord or organ was written with the intention of being played on an instrument with two manuals (two keyboards sort of stacked on top of each other.) On such instruments the hands/voice can play unisons or cross. Playing such music on a piano will be a problem, because there is only one keyboard.
Just to add to Tim H excellent answer. Piano music often has several different voices in the same piece. It would therefore not be all that uncommon for two voices to play in Unison.
Don't let that confuse you though. You just play one note just as normal and then let the two melodies separate again.