Before I Buy,
Is Unreal Game Play all bouncing / Jumping or can I keep my Feet on the Ground ??
Old Eyes !

It depends on the Unreal game.

Unreal Gold (the first game)
is a single player game with occasional jumping mainly to solve puzzles or get to a specific spot.

Unreal 2
is a single player game similar to the first, but with more emphasis on story and slower movement. The jumping is weak and is mostly unused.

Unreal Tournament
is a multi-player game that can be played by yourself using bots (computer controlled characters). It's an arena shooter. This game has lots of running and jumping, no real story (there's one tacked on, but you really just pick a character and play). This might be too much jumping around for you.

Unreal Tournament 2004
Similar to the first Unreal Tournament, it's a lot of running and jumping in an arena shooter.

Many Thanks

Multiplayer Unreal, even if we can jump, is not a rabbit game like other multi shooter games: jump is almost useless to evade bulets. It's nor a ski/jumpjet game.

Monoplayer Unreal game is not a platform game, even there may be some holes we may fall in.