I think you have some errors in the output table you put together here, but I think this modified code should accomplish what you're after. I also rearranged some things so it only opens the insert cursor once.
def main():
import arcpy
import os
# Local variables
sourcegdb = r"N:\TechTemp\BlakeT\Work\TEMP.gdb"
table_in = os.path.join(sourcegdb, "SegmentSequence")
# Create output table
arcpy.CreateTable_management(sourcegdb, "SegmentSequence_output")
table_out = os.path.join(sourcegdb, "SegmentSequence_output")
arcpy.AddField_management(table_out, "UniqueID", "SHORT")
arcpy.AddField_management(table_out, "Begin", "SHORT")
arcpy.AddField_management(table_out, "End", "SHORT")
arcpy.AddField_management(table_out, "SegmentItems", "TEXT", field_length=255)
# Identify observation groups
sqlprefix = "DISTINCT UniqueID"
sqlpostfix = "ORDER BY UniqueID"
observations = tuple(uid[0] for uid in arcpy.da.SearchCursor(table_in, ["UniqueID"], sql_clause=(sqlprefix, sqlpostfix)))
fields_out = ["UniqueID", "Begin", "End", "SegmentItems"]
with arcpy.da.InsertCursor(table_out, fields_out) as i_cursor:
for obsv in observations:
# Read item and (begin, end) into dictionary
fields_in = ["ItemID", "Begin", "End"]
where_clause = "UniqueID = {}".format(obsv)
itemsdict = {r[0]:(r[1], r[2]) for r in arcpy.da.SearchCursor(table_in, fields_in, where_clause)}
# Identify segments
allsegments = [i[0] for i in itemsdict.values()] + [i[1] for i in itemsdict.values()]
segments = tuple(sorted(set(allsegments)))
del allsegments
# Identify items in each segment
for enum, seg in enumerate(segments):
try:
begin = seg
end = segments[enum + 1]
except IndexError:
break
seg_items = [k for k, v in itemsdict.items() if v[0] <= begin and v[1] >= end]
# Write segment items to output table
row = (obsv, begin, end, str(seg_items).strip('[]'))
i_cursor.insertRow(row)
if __name__ == '__main__':
main()
