How important were "columnar" strategies in Japan's invasion of China?

In order to judge the success of "columnar" strategies, we need to consider them within the context of strategic goals, and not simply territorial gains, nor the shape of the attack routes; in this their record is decidedly mixed. The reason why we need to consider strategic goals, is because the way you defined "columnar" is a bit tautological. Since the two examples of columnar strategies were campaigns with territorial gains in the shape of a "column", what if these campaigns failed, and the shape wasn't "columnar" - do these cease to be columnar by definition?

Let's compare the success of columnar vs non-columnar actions in China, by placing them within the context of their goals. In chronological order:

• Non-columnar, North China: initially the goals were to establish a buffer territory between China and Manchukuo, to punish the Chinese for failing to suppress anti-Japanese sentiment, and hopefully repeat the performance of the Mukden Incident. Towards those goals, the outcome was mixed: as fighting escalated, Japan were undefeated as they made tremendous strategic gains (like Taiyuan), but at great cost if you consider this to be the cause of being dragged into full-scale war with China, which ended in a quagmire. Still, if you assume war with China as a foregone conclusion, the verdict is: good.
• Columnar, Shanghai/Nanjing: although Japan was dragged into Shanghai and it lasted longer than they wanted, they did manage to cripple the best, German-style divisions that China had, and the success in Shanghai meant an easy victory in Nanjing, the capital. But another goal, of forcing a Chinese surrender, was not met. Verdict: fair.
• Non-columnar, Xuzhou: as covered in another question, this was a link-up action in preparation for the subsequent attack on Wuhan, and its delay and failure to encircle and destroy Chinese forces greatly contributed to the pyrrhic victory later. Verdict: bad.
• Columnar, Wuhan: despite capturing and holding the city and surrounding territories for the remainder of the war, the battle's duration and Japanese losses meant that this was the beginning of a long period of stalemate, and Japan shifted to defensive and blockading actions. The goal of destroying organised Chinese resistance in Wuhan failed, as the city itself was not contested since the Chinese withdrew as soon as the city was at risk of encirclement. Verdict: bad.
• Non-columnar, coastal regions: these were largely successful in denying supply via China's southern coast, limiting Allied resupply to Indochina, Burma Road and The Hump. Verdict: good.
• Non-columnar, interrim battles 1939-1944: I'm skipping a lot of content here because the fighting had reached a stalemate, with Japan giving up the idea of a swift victory and the focus shifting to south-east Asia (and obviously, the Pacific), plus there were no notable territorial changes. Neither side were able to permanently shift the power balance in their favour during this time. Verdict: fair.
• Columnar, Operation Ichi-Go: despite the dramatic territorial changes, the main objective was to establish an overland supply route to Indochina as the navy was badly losing the Pacific war. In this narrow objective, it was a success. Verdict: good.

So it appears whether strategies were columnar or not had no bearing on their success; there were successes and failures regardless of whether they were columnar.

As for the theory that Japan would have been more successful if they concentrated on getting closer to Chongqing, that's hard to say because it's alternate history. I will note that they did make several belated attempts, for example in Changsha (just upriver from Wuhan) and West Hunan, where if successful, which they were not, would have brought them closer to Chongqing. Their failures were largely due to being spent from Wuhan, which was columnar, but perhaps moreso, location plays a much larger role in the success of strategies. In thinly defended North China and with navy support in Shanghai, Japan achieved success regardless of whether columnar strategies were used, but as they advanced into the difficult terrain of the interior, they were overextended and at greater risk of encircling actions.

Just to make a note, Sherman's March to the Sea is materially different from pushing upriver to Chongqing, as the former is a capitalisation of the victory in Atlanta with a safe destination (since the Union controlled the sea), whereas the latter would be an unsupported penetration deep into enemy territory, with high risk of encirclement and total destruction in case of failure. Instead, Ichi-Go and Xuzhou are closer equivalents to Sherman's action, as they involved linking up adjacent salients.