Links LS 1998 can also work on Windows XP by modifying the regs.cmd file.

Step 0)

Install the game with the offline installer downloadable in your GoG account for this game.

Step 1)

Locate the game's installation directory, for example in:
C:\GoG Games\Links LS98

In this directory locate the file:
regs.cmd

Step 2)
Edit the file with notepad, specifically search and replace ALL the text/String:
/reg:32
with
a single space (" ") (tap the space bar once)

Which is to say, replace the last argument of every REG ADD command with a space in order to remove it.

Step 3)
Double-click the regs.cmd to add the registry keys.

Step 4)
Play the game in your Windows XP PC! :)

NOTE:
IF you do NOT do these steps, then the game will start in Windows XP, but there will be no courses/content available and no way to install it.

For more of an explanation, we can see that the documentation that Microsoft provides, which specifies the following information for REG ADD:

> /reg:32 Specifies the key should be accessed using the 32-bit registry view.

So the consumer version of Windows XP, being 32-bit only, did not have this argument, leading to an error when the command attempts to use it!

learn.microsoft.com/en-us/windows-server/administration/windows-commands/reg-add