On a 2 OS P2P: Can I "share" designate and run an application program on the program-non-resident computer? Explain please.?

As the pictured schematic shows (I hope), if I could share designate application program software (say, the MS Office suite or an Office app) for loading and execution on a remote OS via a computer to computer LAN connection, it might allow avoidance of second Office s'ware purchase to process Office generated files on the "Office-non-resident" computer. (The compatibility features don't work so well in the backward direction...from higher leve Office to lower level Works application.) Or is that not possible. Explain please and thank you. The OS types and pertinent s'ware's are shown in the schematic photo..