ay a game hen breast-side down on a work surface; use kitchen shears or a sharp knife to cut the backbone out of game hen, cutting through each side of the bone from top to bottom. Remove the backbone. Use a sharp knife to slice through the cartilage of the breastbone. Flip game hen breast-side up, flatten bird lightly with your hands, and twist the wing tips underneath the wings. Repeat with remaining game hen.

Place white wine vinegar, vegetable oil, rosemary, orange juice, garlic, egg, Calabrian chili sauce, orange zest, kosher salt, and anchovy fillet into a blender. Pulse several times to combine; blend until marinade is smooth and creamy.

Place game hens into a resealable heavy plastic bag and pour in marinade. Squeeze out air, seal the bag, and refrigerate for at least 4 hours but preferably 8 hours to overnight.

Preheat an outdoor grill for medium heat and lightly oil the grate.

Remove game hens from marinade, reserving marinade. Dry birds on paper towels. Season breast sides with salt.

Place game hens breast-side down onto the preheated grill and cook until skin shows browned grill marks, about 5 minutes; rotate hens 45 degrees and grill for 5 more minutes to make crosshatch grill marks.

Flip game hens onto their backs, brush with reserved marinade, and grill with the lid on for 5 minutes. Brush hens with more marinade. Repeat, cooking for 5 minutes, then brushing with more marinade, until game hens are deep golden brown and an instant-read meat thermometer inserted into the thickest part of a thigh reads 160 degrees F (71 degrees C), about 35 more minutes. Flip hens breast-side down, brush once more with marinade, and cook with the lid closed until marinade has glazed onto chicken, about 5 more minutes.

Transfer hens to a serving platter and let rest for about 5 minutes before serving.