Calling kyokushin "knockdown karate" is not realy accurate. Kyokushin was the FIRST knockdown karate style, but nowdays there are many (who basicaly all derrives from kyokushin in some way) -Ashihara karate, seidokaikan karate, shidokan karate, world Oyama karate, Enshin karate -the list is long.
Unfortunaly kyokushin is very splintered politicaly and the different factions are all fighting each other in courts -there is little or no cooperation.

Also there are NO pro fighters in kyokushin (or most other knockdown karate style) it is strictly amature fighters. the exeptions are kyokushin fighters who has taken up other sports to use their skills in (Filho, Feitosa, Andy Hug etc). but there are no pro knockdown karate circuis.
Knockdown karate is NOT the same as "full contact karate" as it was done in the US.

Technicaly kyokushin is not realy all that different from shotokan or gojuryu (the two karate styles that the founder combined to make the style) and all other karate styles, but when it comes down to fighting it is VERY different.
Kyokushin has drawn some inspiration from thaiboxing in its techniques, but much, MUCH less than thai enthusiast like to claim.

Competition rules are no punches (including elbows) to the head, kicks (and knees) are allowed anywhere exept to throat, groin and directly to the spine. No protection exept a cup. If you down/incapacitate your opponent for more than 5 sec, or twice for less than 5 secs in one round you win. If its a draw the judges _may_ give the win to the superior fighter, but usualy gives extention rounds. Each round starts fresh with a blanc record.
If noone wins after all allowed extention rounds it gets a little complicated. the winner may be chosen by earlier brick breaking (done in between some rounds to qualify to advace) or by the scales (if there is a 10 kg weight difference or more the lighter fighter wins).

In kyokushin no grabbs, grappling or throws are allowed, but some splinter styles allows it to different extent.
In the past there was also grappling from judo (the founder was a friend and sparring partner to Kimura) and jujutsu. But that is almost all gone from training (and totaly gone from competition) in kyokushin today.

Knockdown karate fighting are brutal and inellegant affairs where the opponents snipes at long distances and later sluggs it out in close distance, hopefuly without receiving too much damage to advance in the tournament.
The "no punches or elbows to the head" rule usualy makes it end up in a close distant fight where the fighters refuse to give ground (to avoid looking being pressed backward by a "superior" fighter and possibly loose in a draw).
To outsiders who dont know the game, it tends to look like a primitive slugfest. but its not -there is plenty of tactic and technique involved.
Foot work is usualy very good when the fighters not are stuck in close combat punch-lowkick trading.