Well...organic chemistry for one, really likes stability, or so I believe. It may go through less stable states(RDSes of the respective reactions) to achieve that stability.
Here OPP is a good leaving group. It gives linaloyl pyrophosphate a chance to form a six-membered ring, which is thermodynamically miles ahead in stability than the open chain-form it was earlier. Looks like a cope-rearrangement to me, just that it isn't a 1,5-diene and is a 1,6-diene. One of the double bonds knocks the OPP out just as simultaneously the other double bond forms the six-member ring.
As someone said to me earlier in these very forums, "intramolecular reactions proceed much faster than intermolecular ones", provided there is scope for an intramolecular reaction. The double bond present in the same molecule acts as a nucleophile in the next step instead of OPP directly attacking as a nucleophile(simply because there is scope for intramolecular attack). Of course there might be by-products where OPP attacks straightaway after the rearrangement of linaloyl pyrophosphate. The intramolecular product would be major.
Now there is no scope for rearrangement. The methyl group cannot migrate to that position, as the bridgehead carbon must not be made planar. Hence OPP can attack.
PS : Just my 2 cents.
Edit : Another example is in the substrate CH
2=CH-CH
2CH
2NH
2, when it is diazotized, and then water is added. The double bond performs an intramolecular attack to form a cyclopropane ring (again here there is a good leaving group in the form of N
2). Then water relieves the carbocation. I figured while doing these types of questions(involving neighbouring group participation or anchimeric substitution assistance) that the group present in the substrate is a better nucleophile than the reagent which is going to attack. Debatably, a double bond is a better nucleophile than water(not hydroxyl ion, water) and hence I could apply NGP.
So I suppose that the double bond is a better nucleophile than OPP here? This is a NGP after all.
Note : There can be ring expansion if heat is provided.