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Many tutorials I have watched say that everything should be made in 'quads' (ie. no triangles, and no ngons).

I think this is mainly due to getting into this habit so that if I make a complex model, eg. a rigged character face, then there won't be any animation issues like model warping or bad occlusions/shadows/etc. (please do correct me if this is wrong, its just what I've gathered from many videos and some books).

So I tasked myself with making a Glock handgun, thinking this boxy shape might be a good starter project. I noticed the corners of the top piece are curved/beveled, so I beveled it on my model.

This is where I got my first problem though, the bevel process created about 3 new vertices on each corner I applied it to, but then this leaves the side of the piece with more than 4 edges (see picture):

Image of Glock model

In the pic you can see I highlighted one of the small 'edges' the bevel created. So now I can count something like 12 edges in total surrounding that side part.

Is that an ngon? Will it matter? And if its not OK, how should I do it?

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Is that an ngon?

It is a polygon with more than 4 sides, so yes, by definition, it is an ngon in this sense.

Will it matter?

Probably not.

As you say, non-quad faces can be troublesome when applying smooth deforming animations, but this is a rigid object that won't need to deform in that way.

Non-quads can also cause trouble if you want to apply subdivision modifiers to smooth an initial control mesh, or to apply surface sculpting & high-res detail through something like Z-Brush/Mudbox. But that doesn't seem to be part of the workflow you have planned for this object.

In gamedev, the most surefire way to know if something is a problem is to try it and see what goes wrong. If nothing's gone wrong yet, then it might very well be good enough for your purposes. ;)

And if its not OK, how should I do it?

Finding a good edge flow for quads on a mesh that needs animation or subdivision is an art form in itself. An artist-focused site like Polycount might be a better place to get detailed guidance on this front. Check out their forum posts about edge flow, and hard surface topology

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