If it is to be usable in daylight, it should be completely glossy like a smartphone screen.
I don't think it is obligatory: on
we have seen a Thinkpad with brighter glossy screen with problems under daylight (not direct sunlight, but daylight), while other with matte and darker screen did a better job.
Obviously if you think on a matte display with even less bright you can have problems, but that isn't correlated to matte display, as they can be bright enough if it is designed so.
Personally, I don't think matte is an advantage, when I use a glossy screen on my phone I find it usable in most light conditions.
My smartphone can get very very high bright (with "AUTO" mode), and can compensate under daylight, but reflections are uncomfortable under a lot circumstances.
In my experience sing a computer with a glossy display (even glossy plastic around display) is very uncomfortable. I prefer matte display without doubt. And if you look to most professional monitors (may be Apple excluded

) you will see most have matte non-reflective displays. Even casing is matte (I remember a workplace where we had matte display but bright plastic casing, and reflections on that case was disturbing).
Modern smartphones have capacitive touch screens, and all capacitive screens I have know about are glossy (I don't know if it'd be possible to make a capacitive screen without glossy, but I have never seen one).
Only one of my notebooks have a glossy display (it is convertible tablet-ultrabook and has capacitive touch screen) and it is good if you don't have bright images or lights behind, because when you have them that glossy display is a torture.
I suppose in an office environment you can have a lot of sources behind (cell lights, windows...).
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The CPU design in this netbook I'm still using will hit 10 next quarter, and I suspect I bought it soon after launch so I'd expect the machine itself to be 10 by christmas. The CPU design in my build machine is actually 10 this quarter, and just old enough not to be hit by spectre attacks I suspect, but I suspect the machine itself hails from a year or two after that.
If it has an Intel CPU only some models of Atom, lowest ones (usually with no more than 2GB of RAM), are immune to Spectre.
In
https://www.techarp.com/guides/complete-meltdown-spectre-cpu-list/ there is a list (you can look at this sublist:
https://www.techarp.com/guides/complete-meltdown-spectre-cpu-list/7/ where you can find Atom models). But I think this list is not complete: they are not showing very old CPU, because it is too much old. For example it seems that even Pentium III and II and even Pentium Pro would be affected.
It may be simpler to look at a list with no affected CPU

For example:
https://forum.level1techs.com/t/list-of-cpus-most-likely-immune-to-spectre/123128
Early Intel Atoms including S/D/N Series: Diamondville, Pineview, Cedar View.
It is amusing that Itanium (IA-64), the architecture Intel wanted to success x86 to go to 64 bits (losing direct compatibility [1]), is totally immune to Meltdown-Spectre. Datacenters running Itanium can be happy now.
PD: All Raspberrt Pi are immune to Meltdown-Spectre bugs.
[1]: Some Itanium had hard support to translate x86 to IA-64 but performance was bad.