OK, it looks like I got the reason I have problem from here.
"
If you use the 64-bit odbcad32.exe to configure or remove a DSN that connects to a 32-bit driver, for example, Driver do Microsoft Access (*.mdb), you will receive the following error message:



The specified DSN contains an architecture mismatch between the Driver and Application



To resolve this error, use the 32-bit odbcad32.exe to configure or remove the DSN."

But the DSN used for queries from Excel files isn't user-defined! It was installed by MS Office Installer! So MS Office Installer didn't check, is there 32-bit or 64-bit OS? And no update or SP didn't correct this either?

The problem isn't that the query doesn't work properly in my computer - I can cope with this. But there are somewhat 200+ MS Office users in our plants all over 4 European countries, and any of them my need to use some of workbooks I have designed. When I go to bosses, and say: "Khm...! We have to employ some guy who will manage all those ODBC datasources!", then I hardly can expect some positive response :-)