For the granita, combine coarsely chopped watermelon and 60g sugar in a bowl and stand until macerated and juicy, about 45-60 minutes. Blend in a food processor until smooth, then pass through a muslin-lined sieve. Transfer to a shallow 20cm x 30cm metal tray and freeze, stirring and scraping occasionally with a fork, until crystals form and granita is frozen (about 4-5 hours).
For the ginger syrup, combine the remaining sugar with ginger and 60ml water in a saucepan and stir over medium-high heat until sugar dissolves. Bring to a boil, remove from heat and stand until cool. Strain and refrigerate until chilled.
Serve the granita in a large, chilled metal dish along with bowls containing the diced watermelon and ginger syrup. Provide chilled glasses and allow guests to help themselves.