There are a few ways to do this, and I'm assuming that the metrics you want to track are largely those available in the Team page.

Central to each approach is needing a way to:

1) Add members to a temporary team 

2) Report on each temporary team's performance

Options that come to mind from simple to advanced.

1. Call Categories
2. Salesforce
3. Spreadsheet
4. BI App

Option 1 - Call Categories:

• Create a call category for each team (e.g. Spring Training - Team 4)
• Put each team member as a "CALL PARTICIPANTS" (and most likely "HOSTED", depending on what you want to measure), and enter any other metrics to constrain on specific calls.
• Select the team name from the Category dropdown for each team to see your metrics
• Select the time period, which likely will be custom 
• Select "Everybody" since people span defined teams

Pros:

• Fast. Easy, Everyone that can see the Team page can see it

Cons: 

• Since it's a temporary/ short term competition you will likely want to delete the Call Category at some point and you will lose the data. (Note: You can always export the results beforehand) 
• If you have more than 1 team, you don't see more than one team at a time 
• Since you need to select "Everybody" you see other people in the list albeit with zero values, so you need to sort to make sure the team members stats show 

Option 2 - Report in Salesforce 

If you are using Gong for Salesforce, you could report on team performance in Salesforce

• Use a field on the user record to assign users to a specific team (e.g. Spring Training - Team 4)
• Someone with the right Salesforce report creation skills will be able to create a report incorporating this user record value with the Gong Conversation objects value 

Pros: 

• If you are using Salesforce people will be comfortable with this

Cons: 

• You need to create the report. 

Option 3 - Use A Spreadsheet 

If it's not too inconvenient you could periodically (daily) export a CSV from the Calls Tab, into a spreadsheet like this mock up example I created. (I've excluded all but a few columns).

• Maintain the team definitions in the spreadsheets Team tab
• Use that definition to map to a populate a "team" value on the spreadsheets Calls tab
• Create a pivot table to report on the team . See the “Pivot Table” spreadsheet tab

Pros

• Easy, Flexible. (Add whatever columns you want from the Calls export list)

Cons: 

• Leaving the Gong app
• What is the best way to make the spreadsheet widely available
• Need to download the data (although this can be automated with some low cost options) 

Option 4 - Use Your BI Tool 

While an advanced topic, if you happen to be pulling data from Gong to a Business Intelligence tool you could store the team definitions in the BI app, and report from there. 

Hope this helps. My vote is for #1. Looking forward to other suggestions and something I may have missed.