Riddle of Kings at War

I think this is about

In a duel between naked kings
he who has a castle and steed shall prevail;

wrap the battlefield in and around itself, however,
and you'll find this is no longer the tale;

but before so doing, add a twist (actually, two!)
and you may find that as before,
our combatants no longer coexist.

However,

... Apparently I'm meant to prove this. OK then, let's have a go. The first thing is that

Now

First of all,

Then

Then

And now

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