^^ By sharing the connection as you’ve described, he *is* bridging the connections, via ICS. ICS creates a bridge + a (software) router. But that's overkill since he already has a router (at least having a wireless adapter and his own network strongly suggest he does). It puts the Win98 machine behind two firewalls and double NAT’s it, which unnecessarily complicates the configuration. Using ICS only makes sense when there is no other router in the picture (i.e., the machine sharing its internet connection has the public IP).
As far as the crossover cable, as long as one machine supports auto-sensing MDIX, a standard cable is sufficient. But yes, in the off chance NEITHER side is auto-sensing MDIX (pretty rare these days), you'd need a crossover cable (or if you have one, just use a spare switch/hub (even an old router, as long as you disable its DHCP server) and connect them indirectly).