The main reason they are using the buckets is to delay sorting costs as far as possible into the future so that there is less cost for most timers (as most timers are apparently deleted far before expiring). I'd suggest that the major performance gain is due to this lazy sorting, and not because their data structure avoids page faults. (Well, it does avoid page faults that the old linked list algorithm would have caused, but these page faults are due to the sorting going on in the original code which is avoided in the second. If timers did not expire, the two approaches would be quite similar, both generating page faults when sorting the linked lists, which likely have bad locality, and neither being as good as an IO-efficient algorithm.)
Using timer wheels as a heap structure wouldn't be appropriate unless many of the objects placed in the heap are removed prior to making it to the top of the heap. If this is not the case the sorting of the items from one bucket to the next bucket (sorting a linked list) would cause many page faults if the list didn't fit in internal memory. Timer wheels do nothing to address data locality which is the main problem faced by extremely large heaps. Your mention of in-order access is only true if the lists at each bucket as indeed stored sequentially in memory. This is hard to guarantee unless that space is reserved ahead of time or some dynamic reallocation scheme is used. I read the linked article as implying that simple linked lists were used, which generally have very bad data locality. Even if if a linear list was guaranteed, however, the sorting step when pushing things from one bucket down to the next bucket would incur page faults (assuming the list was too big to fit in memory) unless an I/O-efficient or cache-oblivious sort were used. (Which could easily be done, making an IO-efficient timer wheel structure.)
The algorithm discussed in the article is for a general purpose heap. In most heaps the main cost is in removing elements from the root of the heap as they bubble up through it, rather than deleting them prematurely (as is the case with timers). Different approaches for fundamentally different problems.