I'm surprised it got as far as the shelf Chris

........... but agree it's an interesting piece.
sorry, don't think I'm going to agree with your explanation for its small size................ only my opinion, but condiment bottles are more likely to have been cut rather than delicately wheel engraved, and early C19 examples often have decoration - around the lower portions - in the form of blazes or slice cutting.
As for the idea of a drinking glass/tumbler - this is a possibility. Tumblers of short stature appear to fall into two groups .... those down around the c. 5 cm. mark like yours are simply called small, and then there are the real dinkies that are called miniature, which can go down as far as c. 3.5 cm.
But .... my thoughts on this being a tumbler/drinking glass are troubled by the cutting on the actual rim............. tumblers can be cut or engraved to an amazing extent on their curved surfaces, and even the base, but the rim itself is usually left smooth.
I can't see on this one if the rim has been fire polished or if it has a Continental type of cut flat rim.
If you look at Barbara Morris 'Victorian Table Glass & Ornaments' - plate 46 (chapter on engraved glass) you can see your 'bulrush'pattern on some wine glasses from James Powell, which are dated to c. 1865 ............ they always looks to me like 'pulled carrots'

The same pattern can be seen in colour plate 9 in Hajdamach's 'British Glass - 1800-1914' - a page from a Richardson design book c. 1845 - 50, where it appears on the neck of a vase.
Whether this particular part of the design was specifically a Richardson invention I've no idea, but both these references would indicate - possibly - that your glass may have its origins in the middle third of the C19, when wheel engraving was at its height.
Of course, if this 'bulrush' design if more ancient, then perhaps your glass may be equally so.
Not sure that I can add anything of real use - it could be a tumbler, or how about a salt - could it be missing a lid do you think?? How about a mustard?