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