While I haven't watched the replay yet, I've done similar things in the past myself. The thing is that the Marza has relatively high DPS for a starting capital ship and can in fact clear a world of militia (provided there aren't too many and the enemy isn't too close). This will leave it damaged afterwards, and so researching repair bays is pretty much mandatory. In fact, if you destroy the siege frigates first you can sneak in a colony frigate, colonize the planet, and build a repair bay while you're still fighting the militia.
A strategy like this works only against militia, however. The only militia units that deal more than marginal damage to a capital ship are LRM's and Kodiaks. Simply put, it doesn't have enough of these to threaten a capital ship, which is why the capital ship on its own can bring down a neutral world. A player, on the other hand, is going to build lots of LRF, and they're going to be lead by a capital ship of his own.
There is no question that a Marza that can fall back to a repair bay is a powerful attacker and defender, but against a well designed early game fleet it will die. I suspect in this case that Cykur may have started in a position where his enemies were too far away to rush, or he would already have LRF by the time their forces arrived.
This doesn't work with a Progen (at least not well) because it's a low DPS capital ship and it takes positively ages to get through even a small militia. It will work with the Akkan. I don't know why you'd try it with the Sova or Halcyon. The Sova is probably better off embargo rushing and using the extra cash to build a strong early game fleet. The Halcyon just is such a trade-off from the progen that I can't see it being worthwhile. In fact, you'll definitely save more from the Progen's colonize ability than the Halcyon could theoretically save you on disciples. However, the Kol and the Space Egg are both great at this.