What is proximity effect?
I will not attempt to define "proximity effects" in my answer. If you are looking for a definition, this is probably not the best answer. I think the term itself is quite vague and rather qualitative if you will. I've personally seen the concept of "proximity effects" being used more in chemical biology / enzymes chemistry context, than in organic chemistry. 

In the first example, I am not even sure if there is indeed any proximity effect in operation. There could be; but it really depends on the solvent effects. How does one really separate the different factors in play? Doing gas phase simulations could give you an answer. The first example you have cited, can indeed be more easily be explained in terms of relative stabilities of the "carbocation" resonance forms: it is more favourable to have the positive charge at position 2 (allylic, secondary), than to have the positive charge at position 4 (allylic, primary). In terms of resonance or MO theory, this picture translates into position 2 being more electron deficient than position 4. A nucleophile would attack at the most electron deficient position (ceteris paribus), and this would be the fastest reaction path. Attack at position 2 leads to the kinetic product, as shown in the book you've cited. Whether there is any additional "proximity effects" - such as the nucleophile being "closer" to position 2 than position 4, is up for debate and cannot be concluded from this result. On the grounds of carbocation stabilisation alone, the observed product can be explained. Note however, that under the conditions, this reaction could be reversible and eventually generate the more stable thermodynamic product. 

The second example, is perhaps a more appropriate application of 'proximity effects'. However, I'm not sure if it is appropriate to call this an 'enthalpic phenomenon'. I would have guessed a more probabilistic/entropic origin of this phenomenon. In this example, I would interpret proximity effect as simply the fact that if you are doing a 1-3 ring closure (to form a 3 membered ring), your two reaction centres are closer in space, and hence the reaction is probabilistically more likely than a 1-6 ring closure. I don't know how using the term 'proximity effect' helps give a better explanation, though. If you're interested, you should read up on rates of ring closures in a book of your choice, that discusses both enthalpic and entropic contributions to analyse the relative rates of ring closure.