I was reading about this recently, and one commentator believed Nixon was camping it by playing the song in a very mock dramatic way, and another commentator noted that his method of playing was closer to a Sunday School teacher than a musician and presumed Nixon was just a crass amateur.
I'm pretty sure this was VERY late in the Nixon Presidency. This may have been his last public appearance as president that wasn't all about Watergate, his final desperate attempt to rally the Base.