Yes, as a rule it does: if you damage another person's smartphone, that is classic third-party damage – exactly what your private liability insurance is there for. The device's current value is reimbursed, not the new price.
Two things you should know: first, liability insurance never pays for your own phone. Second, your policy matters if you were holding the phone as a favour (e.g. to take a photo) or had borrowed it – good policies explicitly include favour damage and borrowed items. How the claim report works step by step and what insurers look for is shown in our guide Filing a Claim: Dropped Phone.
Damage happened? Report it online directly or via WhatsApp (+49 151 28937141).