Just throwing a few things into this discussion for considerations:
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1.
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A lot of European trainers that I have worked with, simply regard K-1 rules as Kickboxing.


2.
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On the most recent K-1 World Grandprix, there was quite a switch from several years ago. By this I mean, back the the 'old' days it was

'Kickboxing' ( Generally Muaythai fighters)

vs

'Karate'.

Now we have KICKBOXING vs M.M.A. - with all of the K-1 Fighters from Muaythai or Karate schools being seen as the 'Strikers' with their 'Kickboxing' skill sets vs the new enemy / rival 'M.M.A.'

Some of the 2009 marketing by K-1, was...

... surely the most prestigious Kickboxing championship could not be allowed to be captured by an M.M.A. fighter ( Alister Overeem ). Especially after Overeem K.O'd 'Kickboxings' Badr Hari. Hence the delight for K-1 that Semmy Schilts is once again the K-1 World Grandprix Champion.

This is quite significant, after K-1 tried to dump Semmy, but shows how important it was that an M.M.A. fighter did not capture the Crown of Kickboxing.

3.
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Another thing I would like to add.

SeidoKaiKan 'KARATE' developed the K-1 ruleset.

Seido was once Kyokushikai, known as the strongest/toughest Karate due to its hard-contact competition format and tough training regime. Many of the top Dutch Kickboxing fighters and trainers have connections to Kyokushinkai.

Basically the rules for Kyokusinkai Kumite competitions, known as knockdown allow:

Kicks, Punches, Knees ( with restricted clinch ).

- although the Punches are bareknuckle and not allowed to strike the head.

You compete more than once in a tournament.

No grabbing or holding ( ie catching the leg ).

Holding Knee-Kick ( hiza-geri ) is allowed only with one hand cupped behind the neck.

In the event of a draw, you do an extra round.

The above Knockdown Karate rules may sound familiar to the K-1 rules, because they are.

K-1 rules are actually seen by some as ' Modified ' Karate rules, as the Knockdown rules were modified to add the wearing of gloves and allowing punches to the head.

Obviously this did become a middle ground for 'Muaythai' Kickboxers and for Knockdown 'Karate' fighters. I just wanted to point that out.

Modified 'Muaythai' to some. Modified Knockdown-'Karate' to others.

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Have seen some use the term ' Japanese Kickboxing ', and also 'Oriental Rules Kickboxing '.

O.R. being used more extensively now in the U.K. by I.S.K.A. which I think is a good thing.