Sorry, but no. DSL and ADSL use frequencies to carry the data which are above the frequencies which ordinary phone lines will carry. Special conditioned lines without load coils must be used, and those lines, when they reach the Central Office, are hardwired to strip off the frequencies used for data and do not allow that data to connect to the Public Switched Telephone Network (PSTN), i.e., the phone system. Therefore, you can't use them as if they were a phone modem; if you need a phone modem, use a phone modem.
Anyway, for gaming, you would not want ADSL, which is Asymmetric. Ordinary (Symmetric) DSL (same speed in and out) is far better for gaming.
If the PCs were within 100 meters of each other, you could skip the ADSL modems entirely and use a crossover LAN cable to connect the computers directly, or use a pair of cables, each no more than 100m long, connected through a hub or switch.
If you need to connect over a distance exceeding 100m, then do the latter; add another 100m cable and another switch to extend the signal, up to a total of 500m without paying telco and without DSL devices of any kind.
Why no longer than 500m? A limit built into Ethernet, sometimes referred to as the 5-4-3 rule: In a network where signals can interfere with each other (the 'collision sense" part of Ethernet), you can have a maximum of 5 segments of bare cable, with up to four switches serving as 'repeaters' to clean up the signals, and no more than three of those switches can have PCs (or other devices) on them, for a signal from any part of the network must reach all of the network in time before it expires.