Prepare grill for medium-high heat; oil grate. Toss squid with 1 tablespoon oil in a large bowl; season with salt and pepper.
Grill squid, turning occasionally, until lightly charred and cooked through, about 4 minutes. Transfer squid to a cutting board and slice bodies into bite-size pieces.
Toss squid with vinegar and chili oil in a clean large bowl. Add cucumbers, watercress, and cilantro and toss to combine. Taste and adjust seasoning with salt, pepper, and more vinegar and chili oil, if desired.