Which upgrades are required for participate in cycle race?
You can ride any bike in a race, provided it's in good enough working order to get you over the line.

Regarding gears, it looks like the cost to add derailleur style gears may be prohibitive, as I assume this bike's rear wheel is single-speed specific and the dropouts aren't vertical (which isn't the end of the world but not ideal). I'd probably either look at a geared road bike, or rebuild your rear wheel around an Alfine/Nexus internally geared hub. 

If this is your first race I'd probably just ride what you have to see if you like riding competitively before spending money on upgrades or on a new bike.

edit: This 'race' appears to be a 200km audax - I'd be incredibly reluctant to do that kind of distance as your first race. Have you ridden over 150km in one hit? If you're super fit, or not bothered about your time you could do it on your existing bike, but a specific road/audax bike would do it quicker and more comfortably. Maybe build up slowly to that kind of distance - that's a very long day in the saddle.