I like the accepted answer by @Lesley, but will add a few things from non-JW sources that may show why their choice of adding "other" multiple times in Colossians 1:15-17 is actually common practice among Bible translators, and the Apostle Paul clarified a similar wording himself. In Hebrews 2:8, Paul says that God "put all things in subjection under his [Jesus'] feet.” For in that He [God] put all in subjection under him [Jesus], He [God] left nothing that is not put under him [Jesus]." One would probably conclude, that if God left nothing that is not put under Jesus, then Paul meant nothing - no exception! That would mean that God subjected himself under Jesus!
Yet, Paul says in 1 Corinthians 2:17 that "when He [God] says 'all things are put under Him,' it is evident that He [God] who put all things under Him is excepted." So it was apparently common language that all did not necessarily mean all without exception, nor that nothing necessarily meant nothing without exception!
The omission of words that express the notion 'other' is particularly common with the Greek word pas (all). This may be seen by comparing verses in the New International Version where a form of the Greek word pas is translated by 'all other(s)' or some similar phrase. In the following listing, none of the verses cited use any of the Greek words traditionally translated 'other'. The word is merely implied by the context.
Matt. 26:35 - And all the other disciples said the same.
Mark 12:43 - this poor widow has put more into the treasury than all the others.
Luke 3:19 - And all the other disciples said the same.
Luke 11:42 - you give God a tenth of your mint, rue and all other kinds of garden herbs
Luke 13:2 - Do you think that these Galileans were worse sinners than all the other Galileans because they suffered this way?
Luke 13:4 - do you think they were more guilty than all the others living in Jerusalem?
Acts 16:32 - Then they spoke the word of the Lord to him and to all the others in his house.
1 Cor. 6:18 - All other sins a man commits are outside his body, but he who sins sexually sins against his own body.
2 Cor. 9:13 - your generosity in sharing with them and with everyone else.
1 Thess. 3:12 - May the Lord make your love increase and overflow for each other and for everyone else
1 Thess. 5:15 - always try to be kind to each other and to everyone else
In all of the above occurrences, the New International Version (NIV) has used words such as 'other' or 'else' to complete the sense in English. This does not mean that they are adding to God's word, they are simply making explicit or clear what was already there in the Greek text. Thus, it is by no means wrong to translate pas as 'all other,' where that is what is implied by the context.
The currently accepted answer by @Lesley already explains why JWs think that 'all other' is implied in Colossians 1:15-17.
In NWT the use of "all other" four times in Colossians 1 cannot be viewed as bias, and it is not interpolation, since the very words of 1:15 reveal that Jesus Christ is a part of creation, which then implies the word "other" in these four places.
In view of the statement in verse 15 that Christ is the "firstborn of all Creation", the New World Translation has a very strong case indeed for its translation. I get that the trinitarian interpretation of Jesus being the "firstborn (prototokos) of creation" is taken in a figurative sense, in that Jesus is the 'pre-eminent' over all creation.
The problem I see here is that there is a koine Greek word used two times by Paul in the bible (1 Corinthians 2:1; 1 Timothy 2:2) that denotes pre-eminence, being ὑπεροχή (huperoché). It's used to describe authority, superiority or pre-eminence - I wonder why Paul doesn't use this term in connection with Jesus' role in creation, if it was this that he wanted to convey. That firstborn was meant literally is corroborated by scripture in Revelation 3:14 (compare to Colossians 1:18), where Jesus as the 'Amen' is called "the beginning of the creation of God".
I know that the trinitarian explanation here is to say that the "beginning" (koine Greek: arché) is to be understood figuratively, as it would denote rulership or Jesus being the "architect", but that is misleading as the word for "ruler" is "archón", and the word "architect" (architektón) also already existed in biblical times (it being used in 1 Corinthians 3:10). My objection to that is the same than with "firstborn" apparently (or conveniently) meaning "pre-eminence" when the actual meaning doesn't fit the trinitarian narrative - why would the common literal word "beginning" which is used in the vast majority of cases in the literal sense denoting the starting point, conveniently mean something different, namely 'ruler' or 'architect' when there are terms used at the time, that much better fit those definitions?
In view of the statement in Colossians 1:15 and Revelation 3:14 that Christ is the "firstborn of all Creation" and "the beginning of God's creation", the New World Translation has a very strong case indeed for its translation.
Of course, it is true that some would render the phrase in Colossians 1:15 as "firstborn over all creation" (New International Version) or even to paraphrase it - incorrectly - as "firstborn son, superior to all created things" (Good News Translation). This is referred to by some as the "genitive of subordination".
It is true that prototokos can at times figuratively refer to supremacy. However, leaving Colossians 1:15 aside, there is no instance of prototokos being used anywhere in the NT or the LXX with a 'genitive of subordination'. Furthermore, even if one accepts the extremely dubious conclusion that Colossians 1:15 has a genitive of subordination, that does still not rule out the possibility of Christ's being a created being. Indeed, in view of the information cited previously in this response, there is no reason why prototokos pases ktiseos could not be translated as 'firstborn over all other creation'!
Jason Beduhn makes an further point in his book Truth in Translation:
So what exactly are objectors to "other" arguing for as the meaning of
the phrase "all things"? That Christ created himself (v. 16)? That
Christ is before God and that God was made to exist by means of Christ
(v. 17)? That Christ, too, needs to be reconciled to God (v. 20)?
When we spell out what is denied by the use of "other" we can see
clearly how absurd the objection is.
The point is obvious: pas (all) does not always necessarily mean every person, human or spirit, who is living, has ever lived in the past or will ever live in the future. Common sense must be applied.
For a more thorough discussion on the subject, checkout the article Does the New World Translation Add Words to Colossians 1:16, 17? and the YouTube video Jesus - by means of him all other things were created | Colossians 1:16.
