(Repeats, without changes, story first published on Friday)
* Game Digital re-emerges after old firm nearly went bust
* Historic firm Thomas Cook fighting back vs online rivals
* Physical stores still have advantages over Internet
* Home Retail Group has also managed turnaround
LONDON, Aug 1 (Reuters) - Europe's traditional High Street retailers are defying the threat from online rivals by making their businesses more efficient and in-store shopping more pleasurable.
Although overall growth trends still firmly favour online shopping, higher share prices flag investor faith in chains such as UK video-game retailer Game Digital, electrical-appliance group Dixons, and Swiss Mobilezone .
Such companies have shut their less successful stores to focus on the most profitable outlets, and have adapted to meet demand from shoppers who, even if they buy online, often want to collect their goods in person.
By contrast, online retailers such as ASOS and even U.S. giant Amazon have had trouble justifying their loftier stock-market valuations: ASOS is down 59 percent year to date and Amazon is down 20.5 percent, reflecting investor impatience over the cost of development plans.
"Against the odds, we think that a number of (traditional retailers) have adapted their strategies successfully and are beginning to fight back against the online giants," said Rob Jones, co-head of European equities at Union Bancaire Privee.
Game Digital is one example: like fellow Brit music-and-movies mainstay HMV, the old Game Group company went into administration in 2012. However, unlike HMV, it revived in a 2014 flotation after shedding half its stores and deepening ties with console-makers Sony and Microsoft. Its shares are up 7 percent since then.
Chains such as Game attract younger teenages who are less likely to use bank cards and therefore less likely to make purchases online, Jones said.
The need for stores to stay relevant for online shoppers has been underlined by the demise of stores that were once staples of shopping streets and retail parks. Virgin has closed its flagship Megastore on Paris' Champs Elysees; British electrical retailer Comet went into administration in 2012.
Electrical goods retailer Darty, whose shares are down by around 30 percent since the start of 2014, has fought back in its core French market by buying a popular website. It posted higher profits in June.
UK clothing retailer Next has profited from a "click-and-collect" delivery scheme that allows customers to collect goods ordered online straight from the store.
This chimes with recent improved performance at catalogue retailer Argos, owned by Home Retail, which said its decision not to cut back its extensive portfolio of Argos outlets was justified because British shoppers were increasingly ordering online and collecting themselves.
Next shares, up 26 percent year-to-date, have outperformed ASOS. Similarly, electrical-goods retailer Dixons is up by around 5 percent, helped by plans to merge with Carphone Warehouse, while online domestic-appliances retailer AO World's shares have slumped 50 percent.
"Physical retailers give consumers the power to decide exactly how they would prefer to shop - something the pure online merchants simply can't compete with," said UBP's Jones.
That pushes online retailers to go physical as well: ASOS has partnered with local convenience stores and newsagents to offer direct collection, while Amazon also offers pick-up spots.
But they still trade at much higher valuations than their physical counterparts, with ASOS at a forward price-to-earnings ratio of 43.92 versus a median of 14.71 for a basket of eight European retail stocks.
Travel agent Thomas Cook, which has reported its eighth straight quarterly profit rise, has benefited not just from cutting costs and stores but also from shopper frustration with increasingly complex online travel sites, investors said.
Thomas Cook's shares are down nearly 30 percent since the start of 2014, but have still outperformed declines of 50 percent or more at online rivals Bravofly and eDreams Odigeo.
Another area that benefits from face-to-face customer relations is telecoms: Swiss retailer Mobilezone has opened new customer help centres and seen its shares rise by nearly 10 percent since the start of 2014.
While figures from the UK-based Centre for Retail Research show that online retail sales in Europe grew at double-digit rates in 2013 versus flat-to-negative rates at physical stores, strong brands are able to mix the two to their credit.
"These companies have successfully transformed themselves while maintaining their traditional High Street presence," said Andrea Williams, fund manager at Royal London Asset Management. (Reporting by Sudip Kar-Gupta; Editing by Lionel Laurent/Ruth Pitchford)