Yes, 'clock' = 'zegar' is standing somewhere in your house (or you see it somewhere outside your house), while 'watch' = 'zegarek' is something you carry with yourself.
Should this not be tamtego? as tego is the accusative form of ten which is the nominitive form? e.g. ten pies & lubię tego psa
Accusative is the only case where it is important whether a masculine noun is animate or inanimate.
If it's animate, the Accusative form looks the same as the Genitive form. "Lubię tego psa. Nie lubię tego psa."
If it's inanimate, the Accusative form looks the same as the Nominative form. "Ten zegarek. Widzę ten zegarek."
You have to also remember that many food articles, especially fruit and vegetables, are considered grammatically animate, although there isn't really any logic to it.
surely this translation should be - do you see that clock. one could hardly ask someone to see a watch unless at a jewellery store
And what's wrong with the store interpretation? As said before, "zegarek" is a watch.