How much linseed oil is needed to treat a beechwood counter top?
The oil that you use (or are thinking of buying) will typically list the coverage on the package or instructions as BMitch suggested in the comments.

For instance, on the website you linked to for the instructions, they sell this (randomly chosen by me, no endorsement) counter top oil, and in the description it says:


  One litre covers approximately 13 square metres per coat. It is touch dry within one hour and can be recoated within three hours depending on temperature and humidity.


So this 500ml can will cover 6.5 square meters, or give your 1 square meter surface about 3 coats.  You mention the depth of the counter top, but that shouldn't matter.  The oil is largely a surface treatment, and the coverage will not change based on the thickness of the wood.

It's been my experience that the first coat might "soak in" more than the additional coats, so the coverage won't be as high as advertised.  In the case of this oil, I would worry that a 250ml can wouldn't be quite enough, so I'd get a 500ml and feel good about having some extra for later.

Of course, look at the coverage on the oil that you want to buy and do the calculations for yourself.