I wonder if this will bring an end to Magical Express? The whole point of ME was to keep you in the world with no rental car. This would effectively do the same thing. Disney could offer discount tickets for the ride, not free of course, and you still would be locked in at Disney. They would have to provide some sort of luggage service as the busses at DS would not be able to accommodate it. I'm sure that Disney pays a pretty penny to Mears for ME.
Although one could conceivably ride Brightline from MCO to WDW, it seems unlikely that they would eliminate DME.
DME was created as a one-seat ride to connect the airport to the various hotels. However, taking the train would require multiple transfers, using the automated peoplemover from the airport terminal to the multimodal station (in addition to the one taken from the gates to the terminal), train from the multimodal station to the WDW station, and then a bus from the WDW station to the hotels themselves. It's just not especially convenient, especially when you factor in luggage for each transfer, along with the propensity of tourists to screw things up any time they have to take their fate into their own hands. While it can be annoying how often the DME folks check and re-check your destination, their system is well designed to be idiot-proof.
Additionally, with all the transfers, I don't imagine this could possibly save any time when compared to a coach bus. Even when the buses are running infrequently and stop at multiple hotels, the total time from the terminal to your hotel would likely be faster than the multimodal extravaganza this would require.
Furthermore, this train system is designed for long-distance intercity travel, not short-distance local trips. The headways between trains will be more similar to flight routes from an airport than a subway system. During peak periods, trains might run every half hour or so, but could dwindle to 1.5-2 hours between trains during other times of day. While high-speed trains often have several stations in major cities to get long-distance passengers closer to various destinations, they're really just not suited for this type of short trip. Areas with established high-speed rail systems (Japan, France, China, etc.) rely on local bus and subway systems for local trips within any given city.
The only way I see this replacing DME is if Brightline manages to negotiate a contract with Disney at a lower price per passenger than Mears currently has. However, with the huge amount of fixed infrastructure for rail to build and maintain when compared to coach buses that use roads maintained by others, I doubt they'll be able to come close.
Realistically, this station is designed for travelers coming from other Brightline destinations (Miami, Tampa, etc.), as a way to get them closer to their ultimate destination in WDW. It's a convenient enough location that it could convince long-distance travelers to use the train instead of driving; it's the type of anchor destination that really gives the system a reason to exist (unlike the airport station, which is only convenient due to the amount of space available, rather than proximity to anything of interest). Any intracity travel within Orlando would be an ancillary benefit, not a primary goal.