Sadly, everyday computer screens are unable to show you what 670nm red light actually looks like. It is because of the primary colors that a computer screen can display. It cannot display a deeper red color than the red primary color.
Color space standards used for computer screens and video are not the same, but those used for video can be used to explain the issue:
(1) HD video - Rec. 709 (612nm red primary)
(2) Digital Cinema - DCI-P3 (615nm red primary)
(3) UHD video - Rec. 2020 (630nm red primary)
Many computer screens and TVs have a decent coverage of #1, some also #2, but #3 is not that common. #2 and #3 are often called wide color gamut. Even if a computer screen supports wide color gamut, it is unlikely that its red primary color is any deeper than the red primary colors mentioned above.
This website has a lot more information about color spaces, I found it quite interesting:
https://clarkvision.com/articles/color-spaces/