Does SENTRI include TSA Pre-Check for Non-US citizens that are not from one of the following: Colombia, the United Kingdom, Germany, India, Panama, Singapore, South Korea, Switzerland, and Mexico?
No (click "Learn More" under SENTRI), unless they're a US permanent resident:
Access to TSA Pre✓® expedited security lanes at airports within the U.S. and U.S territories for U.S. Citizens and U.S. lawful permanent residents.
However the list of citizenships or nationalities that can get Global Entry (and thus both SENTRI and TSA Pre access) is slightly different than the one in your question. The current list is: Argentina, India, Colombia, UK, Germany, Panama, Singapore, South Korea, Switzerland, Taiwan, Mexico.