In fact both WiMax and LTE are becoming available at the moment. WiMax has the edge when it comes to handsets but LTE deployments are starting in Europe.
You're right to point out that there isn't that much of a battle but that's because the two technologies are actually very similar. While WiMax has the advantage of already being available in some parts of the US, uptake is going to be very slow. LTE has the advantage of allowing more reuse of existing infrastructure. And, with networks increasingly contracting out network management to suppliers, rollout should happen quite quickly. LTE also has the considerable advantage of coming out of the major networks talking shop: they've been able to ask for what they want.
As for which "brand" will succeed over time, well the market will decide that. But it's unlikely to be on technical merits. The argument that competing technologies will deliver the best product at the best price doesn't really hold water. It gave us the VHS cassette and the ISA bus. Given the costs of the R&D and deployment it is also too risky to try out which is why wireless technologies are converging. Sprint/Nextel didn't drop IDEN for technological but economic reasons. And GSM's predominance was also down to economic reasons. Initially GSM was totally unimportant in the US but GSM/UMTS is now the dominant technology in the US.
The networks will accept anything that can be put on a single chip. Intel's undoubted engineering prowess should help adopters there but seeing as there are very, very few handsets with Intel radios that is a handicap at the moment but if Intel can convince manufacturers to use it's systems that could change very quickly. UMTS showed that the demand for the highest possible data speeds was not that great: very few people were prepared to buy new devices and pay premium tarriffs. Only when prices dropped significantly did use take off. Ironically the notional competition from the technically inferior WiFi was important in setting price expectations. Those same expectations are there as the various HSPA upgrades and LTE are rolled out.
So as the article points out: WiMax is likely to be more interesting for places without much existing wireless data coverage. But for established markets it does look very much like the barrier to entry is too high and the window of opporunity too small. This is reflected in the very poor take up of WiMax licences in the countries that tried to auction them.