A part of the page is spawning over the buttons as if trying to mimic the ever growing rocks in front of R2D2, in a few months we (or maybe just I) may not be able to click them anymore.
I have attached and image.

Ctrl-Zooming in and out does not help, using Microsoft Edge instead of Chrome does not help.
At certain zoom levels the buttons are completely gone.

Is there any way to fix this?

Looks like an error either in the font size (#templateStaContainer overwriting the default size) or in the br tag that breaks the line between your and GOG.com.

Firefox and PaleMoon have an option to zoom only text rather than the entire page, that should help.

The problem is probably the kerning or tracking of the font, and how Windows renders it, causing the lines to be slightly too long and spill over to the next line (the text becomes 4 lines on the browsers I tested Windows 10, and 3 on ArchLinux).

EDIT: Also, removing the rather unnecessary linebreak between "your" and "GOG.com shelf" would fix it. Then the font rendering differences between systems wouldn't matter.

It was probably an oversight during the last website redesign.

For easy reference, the direct links are here:

Windows: http://static.gog.com/download/d3/stable/Setup_Downloader_3.6.0_stable.exe
Mac: http://static.gog.com/download/d3/mac-stable/GOG_Downloader_1.2_512.zip