I see “The Battle Hymn of the Republic”—which is not really a hymn, since it doesn’t directly address a deity—as being a gospel song aimed at inspiring Christians to engage in spiritual warfare against the forces of Satan.
That’s how I see it, too.
The only thing “gospel” about it is a false gospel.
Here is what the Apostle Paul says about anyone teaching a false gospel:
“But though we, or an angel from heaven, preach any other gospel unto you than that which we have preached unto you, let him be accursed.As we said before, so say I now again, if any man preach any other gospel unto you than that ye have received, let him be accursed.” (Galatians 1:8-9)
Please read the historical and biblical analysis of the song I linked above.