Each player must send monsters from his/her side of the field to the Graveyard so that he/she only controls 1 Type of face-up monster. As long as this card remains face-up on the field, each player can only Summon or control 1 Type of face-up monster at a time.

Now just re-read the text, and think about how useful this could be.
This card works wonders if you run a theme-deck. At present I am running a twist on the Dragoon control concept, using destiny Dragoon and another huge fusion monster with chain material and fusion gate to really punish my opponents, and eradicator virus to control draws.

The reason why this card works well for me in my side deck, is that all but 2 of my monsters are warriors, and off those 2, only one of them will ever hit my field. Hence, i effectively only have one monster type to call.

Thats how it benefits me, but how does it cripple my opponents.

Against GB: this is a deck type that tries to abuse the bestari/darius/prisma combo to get gyzara on the field, and finish off with a main pahse tag out for herakalinos.
however, against this trap card, this deck fails massively. All the useful GB monsters are off a different type. Infact with Rivalry of warlords on the field, the only way to pull off the tag out, would be with a face down GB and summon bestari to contact fuse for gyza, something that slows down this deck. Prisma is completely shut out and darius can only summons another darius or laqauri.

But effectively, this slows down the plays a GB player can use.

Against DAD: While a lot of DAD decks use warrior support, this trap if face up, shuts down the rush of multiple monsters on the field at same time.  Admittedly, havinga clear field then dropping DAD itself means your trap is gona bite the dust, but if it looks like a rush going to happen, flipping rivalry will limit what your opponent can summon. This is especially good, if they got for the armageddon knight summon, into DMOC play after a monster reborn.............with rivalry on the field this makes your opponent make some choices about what to choose, and limits the options. You can also use this as a way of keeping 3 tributes off the field and prevent D-plasma hitting the field.

Against Lightsworn: The thing with lightsworn is that again similar to GB they are all different types. lyla and lumina are spellcasters, garoth a warrior, wulf a beast-warrior, ryko a beast and JD, well a dragon. This means hittng you with a rush of lighsworn with rivalry on the field is a little difficult. Additionally if your opponent can not get rid of it, a lyla play before dropping JD is not going to happen easily.

Now im not saying that rivalry of the warlords is the ultimate side deck option for all decks, infact it is a tricky card to play with. Your oppnent can still set cards without fearing its effect, and being a trap is subject to the perils of decree and jinzo. The one benefit I have found using it though, is that which I have mentioned a few times already, in that it stops rushes, and slows down your opponent, what this means is it can give me the TIME i need to win, and in a time when the fastest deck tends to win, stopping that speed in your oppenent can be all you need to do.

Duel away and have fun