I find chess has a very high degree of abstraction compared to other wargames I play. If you are interested in (non-chess) alternatives I recommend you have a look into something like ancient wargame rulesets - a good example is DBMM. There are no square limitations, varying numbers of pieces per side, a much larger battlefield with terrain, varying number of moves per turn, stratagems/tricks for confusing your opponent, stone-paper-scissors troop interactions (a beats b, b beats c, c beats a), gradual loss of cohesion and control as the battle progresses, randomness (in movement and combat) by the use of a dice, and the ability to implement grand strategies and/or purely tactical plays. This game is based on real historical armies from around 3000BC to about 1500AD.
Alternatively, there are other games (and clubs) if you are interested in the Napoleonic period, modern day warfare, Colonial expansion etc etc.