What does it do?
This script periodically downloads your competitive 1v1 duels history from your activities list and stores game results in your browser in a way that they can be queried efficiently. It then uses this data to show you head-to-head statistics (score and elo balance, overall and by game mode) on each player's user page. In addition, when hovering over the head-to-head score, it displays a list of the most recent games against that player (overall or in the respective mode) and links to the respective game summaries.
Why does the download take so long?
You've probably played a lot of duels. The script is designed for all downloads to happen in the background while you can continue to use the site as normal. For this reason, it is somewhat conservative in how quickly it sequences duel downloads in order to minimise the probability that you will be rate-limited by Geoguessr, which could impact the functionality of the site as you're using it.
I've played this person way more often than this! Why is it missing duels?
Geoguessr only allows you to query your activity history for the past year. The script is therefore limited to the duels you have played up to one year prior to you installing and running the script for the first time.
I've just played a duel against someone and the statistics didn't change!
The script checks your activity history at most every hour automatically and so the statistics only update once an hour. However, you can trigger an instant check and download via the userscript manager menu (e.g. Tampermonkey).