Your link is not particularly helpful - perhaps you mean something like https://stats.bis.org/?m=6%257C346%257C644#ppq=CBS_IB_INT_C_BY_SEC_TYP_IB;pv=11~10,9~0,0,0~name
"All countries excluding residents" is a phrase BIS use for international debt securities, so represents debt or similar instruments issued by somebody in one country and held by somebody else in a different country, i.e. excluding residents (human or corporate) of the same county
Note that residents of the same country may have a different nationality or be owned by non-residents. So for example if an American-owned subsidiary incorporated in London issues a debt security to a German-owned subsidiary incorporated in London denominated in Japanese Yen, this would be excluded from these statistics since the two banks are both resident in the UK. But if the American-owned bank in London holds a debt security issued by an American bank in New York, this should not be excluded, and should count as a US liability to the UK
BIS provides a glossary, which is sometimes helpful and sometimes less so