Error 29527: While upgrading from SP1 to SP4 in SQL Server 2005
As per logs you posted 

Products Detected                         Language  Level  Patch Level       Platform  Edition
Database Services (ALCSQLMFG)             ENU       SP1    2005.090.2047.00  x64       STANDARD
Database Services (MSSQLSERVER)           ENU       SP4    2005.090.5069.00  x86       STANDARD
Reporting Services (MSSQLSERVER)          ENU       SP4       9.00.5069.00  x86       STANDARD
Notification Services                     ENU       SP4       9.00.5069.00  x86       STANDARD
Integration Services                      ENU       SP4       9.00.5069.00  x86       STANDARD
SQL Server Native Client                  ENU                 9.00.2047.00  x64       
Client Components                         ENU       SP4           9.4.5069  x86       STANDARD
SQLXML4                                   ENU                 9.00.5000.00  x64       
Backward Compatibility                    ENU                    8.05.2312  x64       
Microsoft SQL Server VSS Writer           ENU                  10.3.5500.0  x64     


If you see it you have two instances installed 


ALCSQMFG instance is at patch level 2047 and is 64 bit standard edition
MSSQLSERVER instance is at patch level 5069 and is 32 bit Standard edition.


Further if you go down the logs you can see message

Database Services (MSSQLSERVER)           Setup cannot update Database Services x86 on this computer. To proceed, run the Service Pack Setup program for the x86 platform instead.
Reporting Services (MSSQLSERVER)          Setup cannot update Reporting Services x86 on this computer. To proceed, run the Service Pack Setup program for the x86 platform instead.
Notification Services                     Setup cannot update Notification Services x86 on this computer. To proceed, run the Service Pack Setup program for the x86 platform instead.
Integration Services                      Setup cannot update Integration Services x86 on this computer. To proceed, run the Service Pack Setup program for the x86 platform instead.
Client Components                         Setup cannot update Client Components x86 on this computer. To proceed, run the Service Pack Setup program for the x86 platform instead.


Now the message is clear you are trying to update MSSQLSERVER which is already at SP4 level and is 32 bit. You are using 64 bit installable to update 32 bit to SP4 which is already at SP4. Seems like you are confused with instances.

What you have to do is 

You need to update instance ALCSQMFG which is at SP1 level to SP4 and since because this instance is 64 bit you need to run 64 bit installable. What mistake you are doing is you are running 64 bit installable but you are selecting wrong instance you have to select ALCSQMFG instance and then proceed with upgrade