Looks like you just need to update the list of files to remove the path, leaving a file name then just append to a new list to use in the InsertCursor. Also, MakeTableView_management is expecting another parameter (you only provided a single "inTable" and it needs the output name of the table view you want to create.
inFiles = ['H:\\file1.txt','H:\\file2.txt','H:\\file3.txt']
inTable = r'\\computer1\home$\user\Docs\ArcGIS\Default.gdb\tabSourceIn'
inField = ['filenames']
rowvalues = []
for file in inFiles:
rowvalues.append(os.path.splitext(os.path.basename(file))[0])
cursor = arcpy.da.InsertCursor(inTable, ['filenames'])
for row in rowvalues:
cursor.insertRow([row])
del cursor
arcpy.MakeTableView_management(inTable, 'outputTableView')