I don't think it would be "stile" since they don't appear to specify the dimensions of any other parts of the gate itself. Presumably the "kit" comprises the gate (leaf) itself and its two posts, the hinge post and the shutting post.

I don't think the 40x40 dimension is a problem either, unless the gate is very heavy. My wrought iron portillon (see profile picture) is actually pretty heavy, though not as heavy as a solid wooden gate, and the hinge post is a 45 x 35mm T section. In its currently location one side of the T crossbard is admittedly chased into the brickwork, but originally (as far as I can make out/remember), when in an overgrown side fence, it had no more support than a diagonal iron brace. The shutting post is new and is a 50x50 hollow section (also now fixed to brickwork).

In any case, it is also quite possible that your gate is not intended to be freestanding, but rather that its posts are designed to be fixed to a wall or a concrete post or braced in some other way.

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Note added at 52 mins (2010-09-13 08:21:14 GMT)
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Here you have a 2"x2" section steel gate post for gates spanning up to 10 feet. A simple side/garden gate could have posts considerably smaller:

"Our 2" x 2" (50 x 50cm) posts are for gates to fit up to a 10' (3.05m) gap. For gates to fit a gap of 10' (3.05m) or over please order the 3" x 3" (75 x 75mm) posts"

Note also " Once you have found your gate height, you then need to decide whether your posts will need to be INSERTED BELOW THE GROUND OR FIXED ABOVE THE GROUND WITH A WALL FIXING"
http://www.cannockgates.co.uk/shop/product/38/Metal-Post-Sec...

Also their preferred terminology:
• Hanging Post
• Latching Post

No specific references, just what I myself would automatically call those things without thinking twice.

* From "cadre".
Le portillon PVC LANGUEDOC est un portillon Plein CDG. Il est livré monté avec sa quincaillerie complète. Son cadre est en Aluminium de section 40 x 40 mm et renforcé par des angles. Le portillon LANGUEDOC est prévu pour une côte tableau (entre poteaux) de 1040 mm.
So, it's not posts (too skinny as someone else said). Tony's "uprights" is logical, but I imagine there are horizontal bits too.