The Modern King James version, published in 1999 has been around for a while, and as far as I know, never sold near the level of the NKJV.
Now I see the MEV (Modern English Version) was published in 2014 and so I expect this is the one the OP addressed.
It (MEV) is listed as one of the 19 versions in the KJV family.
Here is a link:
http://modernenglishversion.com/
And here is John 3:16 according to the MEV: "For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish, but have eternal life."
As you can see, the translation does not reflect near the modern scholarship found in the WEB.
Here is the WEB,
16 For God so loved the world, that he gave his one and only Son, that whoever believes in him should not perish, but have eternal life.
I obtained a Thinline Reference Bible edition of the 2014 Modern English Version published by Passio or Charisma Media.
It shows another 2014 copyright by Military Bible Association.
Its "Preface to the Reader" states:
"Today, realizing the need to update the King James Version for the twenty-first century, forty-seven scholars serving as professors, or chaplains to the Armed Forces of Her Majesty Queen Elizabeth II and to the United States Armed Forces, comprising the Committee on Bible Translation under the leadership of the senior editorial advisor Dr. Stanley M. Horton and the chief editor Dr. James F. Linzey, have joined forces to produce a more updated English edition of the King James Version called the Modern English Version, which is based on a modern English vernacular" (p. x).
Its "Preface to the Reader" also states:
"The Modern English Version is a translation of the Textus Receptus and the Jacob ben Hayyim edition of the Masoretic Text, using the King James Version as the base manuscript.
The Committee on Bible Translation adhered to the principle of formal equivalence, the meaning of which is to be as literal as proper English syntax and grammar will allow" (p. x).