Remove it it is not important

Some punctuation would help here:

I miss you. Not the "I haven't seen you in a while" kind of 'miss you', but the "I wish you were here at this very moment" kind of 'miss you'.

The speaker is distinguishing between the two different things which saying "I miss you" can mean: you can say "I miss you" either to mean "I haven't seen you in a while" or you can say it to mean ""I wish you were here at this very moment".

Each phrase between inverted commas ( " ") is preceded by the definite article ('the') because each one is a distinct, specific definition.

Here's a similar statement:

You're funny. Not the "You're really weird" kind of 'funny', but the "You make me smile" kind of 'funny'.

I hope that all makes sense. Punctuation is important.

Ahmed is correct. The word "the" has no reason to be in the sentence.