1. Question Restatement:
As I understand it, the question is asking if "there I am in the midst of you", (Matthew 18:20) - should be interpreted figuratively or literally.
2. The Context - and The Greek
Matthew 18:1 begins, stating that Jesus' Hebrew name is "Immanuel, God With Us", in reference to Isaiah:
NASB, Isaiah 8:10 - Devise a plan, but it will be thwarted; State a proposal, but it will not stand, For God is with us, (כִּ֥י עִמָּ֖נוּ אֵֽל).
In Matthew 18, Jesus is largely speaking to conflict, and the pursuit of unity, how they should find resolution - To forgive - and to release, (λύσητε, Matthew 18:18) in Heaven and Earth, (Matthew 18:15-20), or exceptionally to bind.
In their midst, (μέσῳ) - Midst also has the meaning of "Between" - which immediately stirred up all of the passages in Scripture with this same idea, (Greek Search). Especially between David and Johnathan in 1 Sam 20:23.
συνηγμένοι - Does mean "gathered together" - but it also sits in the same context as Matthew 18:19, Interlinear - with συμφωνήσωσιν, "chorus of voices", a symphony, unity).
To Petition, αἰτήσωνται - Is inflected in the Greek in the Middle Voice, indicating that the Petitioners are making an appeal to God for their own benefit, (Strong's Reference).
3. Answer - Unity, for The Ministry of Reconciliation:
2 Corinthians 5:18 - Now all these things are from God, who reconciled us to Himself through Christ and gave us the ministry of reconciliation.
Jesus' Words - Were Undoubtedly For Reconciliation:
NASB, Matthew 18:21 - Then Peter came and said to Him, “Lord, how often shall my brother sin against me and I forgive him? Up to seven times?” 22 Jesus said to him, “I do not say to you, up to seven times, but up to seventy times seven.
In Scripture, there are Many Examples of this Term being used Idiomatically, both "positively" and "negatively", ("Judge Between", Biblical Search).
In the Negative Sense:
NASB, 1 Samuel 24:12 - May the Lord judge between you and me, and may the Lord avenge me on you; but my hand shall not be against you.
And in the Positive Sense:
NASB, 1 Samuel 20:23 - As for the agreement of which you and I have spoken, behold, the Lord is between you and me forever.”